asymptotic behavior of trajectories for some nonautonomous almost periodic processes abstract in this paper asymptotics are studied for some almost periodic processes on a complete metric space x d 1 it is shown that any precompact positive trajectory of a contractive periodic process is asymptotically almost periodic as t this property does not hold for general almost periodic contractive processes 2 a compactness result is obtained for weakly almost periodic complete trajectories of some possibly nonlinear processes in a uniformly convex banach space 3 the existence of almost periodic trajectories is studied for affine processes in a uniformly convex banach space these results are applicable to some evolution equations of the form du dt a t u t f t where t is almost periodic r v uniformly convex banach space and a t is a periodic time dependent m accretive operator in v

controllability cost of conservative systems resolvent condition and transmutation abstract this article concerns the exact controllability of unitary groups on hilbert spaces with unbounded control operator it provides a necessary and sufficient condition not involving time which blends a resolvent estimate and an observability inequality by the transmutation of controls in some time l for the corresponding second order conservative system it is proved that the cost of controls in time t for the unitary group grows at most like exp l 2 t as t tends to 0 in the application to the cost of fast controls for the schrodinger equation l is the length of the longest ray of geometric optics which does not intersect the control region this article also provides observability resolvent estimates implying fast smoothing effect controllability at low cost and underscores that the controllability cost of a system is not changed by taking its tensor product with a conservative system

remarks on rates of convergence of powers of contractions abstract we prove that if the numerical range of a hilbert space contraction t is in a certain closed convex set of the unit disk which touches the unit circle only at 1 then t n i t o 1 n with 1 2 1 for normal contractions the condition is also necessary another sufficient condition for 1 2 necessary for t normal is that the numerical range of t be in a disk z z 1 for some 0 1 as a consequence of results of seifert we obtain that a power bounded t on a hilbert space satisfies t n i t o 1 n with 0 1 if and only if sup 1 2 1 1 r t when t is a contraction on l 2 satisfying the numerical range condition it is shown that t n f n 1 converges to 0 a e with a maximal inequality for every f l 2 an example shows that in general a positive contraction t on l 2 may have an f 0 with lim sup t n f log n n a e

controllability and observability for non autonomous evolution equations the averaged hautus test abstract we consider the observability problem for non autonomous evolution systems i e the operators governing the system depend on time we introduce an averaged hautus condition and prove that for skew adjoint operators it characterizes exact observability next we extend this to more general class of operators under a growth condition on the associated evolution family we give an application to the schrodinger equation with time dependent potential and the damped wave equation with a time dependent damping coefficient

feedbacks for nonautonomous regular linear systems we introduce nonautonomous well posed and absolutely regular linear systems as quadruples consisting of an evolution family and output input and input output maps subject to natural hypotheses in the spirit of weiss work these maps are represented in terms of admissible observation and control operators the latter in an approximate sense in the time domain in this setting the closed loop system exists for a canonical class of admissible feedbacks and it inherits the absolute regularity and other properties of the given system in particular we can iterate feedbacks

strong stability of bounded evolution families and semigroups abstract we prove several characterizations of strong stability of uniformly bounded evolution families u t s t s 0 of bounded operators on a banach space x i e we characterize the property lim t u t s x 0 for all s 0 and all x x these results are connected to the asymptotic stability of the well posed linear nonautonomous cauchy problem u t a t u t t s 0 u s x x x in the autonomous case i e when u t s t t s for some c 0 semigroup t t t 0 we present in addition a range condition on the generator a of t t t 0 which is sufficient for strong stability this condition is more general than the condition in the ablv theorem involving countability of the imaginary part of the spectrum of a

kalman filtering with intermittent observations tail distribution and critical value in this paper we analyze the performance of kalman filtering for discrete time linear gaussian systems where packets containing observations are dropped according to a markov process modeling a gilbert elliot channel to address the challenges incurred by the loss of packets we give a new definition of non degeneracy which is essentially stronger than the classical definition of observability but much weaker than one step observability which is usually used in the study of kalman filtering with intermittent observations we show that the trace of the kalman estimation error covariance under intermittent observations follows a power decay law moreover we are able to compute the exact decay rate for non degenerate systems finally we derive the critical value for non degenerate systems based on the decay rate improving upon the state of the art

mathematical modeling in photoacoustic imaging of small absorbers this paper is devoted to mathematical modeling in photoacoustic imaging of small absorbers we propose a new method for reconstructing small absorbing regions inside a bounded domain from boundary measurements of the induced acoustic signal we also show the focusing property of the back propagated acoustic signal indeed we provide two different methods for locating a targeted optical absorber from boundary measurements of the induced acoustic signal the first method consists of a multiple signal classification music type algorithm and the second one uses a multifrequency approach we also show results of computational experiments to demonstrate efficiency of the algorithms

growth orders and ergodicity for absolutely cesaro bounded operators abstract in this paper we extend the concept of absolutely cesaro boundedness to the fractional case we construct a weighted shift operator belonging to this class of operators and we prove that if t is an absolutely cesaro bounded operator of order with 0 1 then t n o n generalizing the result obtained for 1 moreover if 1 then t n o n we apply such results to get stability properties for the cesaro means of bounded operators

new trends towards lower energy estimates and optimality for nonlinearly damped vibrating systems abstract we present an approach based on comparison principles for energy and interpolation properties to derive lower energy estimates for nonlinearly either locally damped or boundary damped vibrating systems we show how the dissipation relation provides strong information on the asymptotic behavior of the energy of solutions the geometrical situations are either one dimensional or radial two dimensional or three dimensional for annulus domains we also consider the case of general domains but in this case for solutions with bounded velocities in time and space in all these cases the nonlinear damping function is assumed to have arbitrary strictly sublinear growth at the origin we give results for strong solutions and stronger lower estimates for smoother solutions the results are presented in two forms either on the side of energy comparison principles or through time pointwise lower estimates under additional geometric assumptions we give the resulting lower and upper estimates for four representative examples of damping functions we further give a weak lower estimate in the sense of a certain lim sup t and an upper estimate of the velocity for smoother solutions in case of general damping functions and for radial as well as multi dimensional domains we also discuss these estimates in the framework of optimality which is not proved here and indicate open problems raised by these results

tauberian theorems and stability of one parameter semigroups the main result is the following stability theorem let t t t tzo be a bounded co semigroup on a reflexive space x denote by a the generator of t and by a a the spectrum of a if a a n ir is countable and no eigenvalue of a lies on the imaginary axis then limt boo t t x o for all x e x

unique recovery of lower order coefficients for hyperbolic equations from data on disjoint sets abstract we consider a restricted dirichlet to neumann map s r t associated with the operator t 2 g a q where g is the laplace beltrami operator of a riemannian manifold m g and a and q are a vector field and a function on m the restriction s r t corresponds to the case where the dirichlet traces are supported on 0 t s and the neumann traces are restricted on 0 t r here s and r are open sets which may be disjoint on the boundary of m we show that s r t determines uniquely up the natural gauge invariance the lower order terms a and q in a neighborhood of the set r assuming that r is strictly convex and that the wave equation is exactly controllable from s in time t 2 we give also a global result under a convex foliation condition the main novelty is the recovery of a and q when the sets r and s are disjoint we allow a and q to be non self adjoint and in particular the corresponding physical system may have dissipation of energy

numerical resolution of an electromagnetic inverse medium problem at fixed frequency the aim of this paper is to solve numerically the inverse problem of determining the complex refractive index of an electromagnetic medium from partial boundary field measurements at a fixed frequency the governing equations are the time harmonic maxwell equations formulated in electric field in a two dimensional bounded domain we express the inverse problem as the minimization of a cost function representing the difference between the measured and predicted fields our numerical reconstruction algorithm combines the bfgs method and an iterative process called the adaptive eigenspace inversion the unknown complex coefficient is expanded in terms of eigenfunctions of an elliptic operator both the eigenspace and the mesh are iteratively adapted during the minimization procedure numerical experiments illustrate the performance of the reconstruction for various configurations

dissipative operators on banach spaces a bounded linear operator t on a banach space is said to be dissipative if ett 1 for all t 0 we show that if t is a dissipative operator on a banach space then a limt ettt sup t ir b if t ir is contained in i 2 i 2 then limt ettsint sup sin t ir some related problems are also discussed

reconstructing initial data using observers error analysis of the semi discrete and fully discrete approximations a new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in ramdani et al automatica 46 10 1616 1625 2010 based on the concept of observers also called luenberger observers this algorithm covers a large class of abstract evolution pde s in this paper we are concerned with the convergence analysis of this algorithm more precisely we provide a complete numerical analysis for semi discrete in space and fully discrete approximations derived using finite elements in space and an implicit euler method in time the analysis is carried out for abstract schrodinger and wave conservative systems with bounded observation locally distributed

sharp observability estimates for heat equations the goal of this article is to derive new estimates for the cost of observability of heat equations we have developed a new method allowing one to show that when the corresponding wave equation is observable the heat equation is also observable this method allows one to describe the explicit dependence of the observability constant on the geometry of the problem the domain in which the heat process evolves and the observation subdomain we show that our estimate is sharp in some cases particularly in one space dimension and in the multi dimensional radially symmetric case our result extends those in fattorini and russell arch rational mech anal 43 272 292 1971 to the multi dimensional setting and improves those available in the literature namely those by miller j differ equ 204 1 202 226 2004 siam j control optim 45 2 762 772 2006 atti accad naz lincei cl sci fis mat natur rend lincei 9 mat appl 17 4 351 366 2006 and tenenbaum and tucsnak j differ equ 243 1 70 100 2007 our approach is based on an explicit representation formula of some solutions of the wave equation in terms of those of the heat equation in contrast to the standard application of transmutation methods which uses a reverse representation of the heat solution in terms of the wave one we shall also explain how our approach applies and yields some new estimates on the cost of observability in the particular case of the unit square observed from one side we will also comment on the applications of our techniques to controllability properties of heat type equations

iterates of markov operators and their limits abstract it is well known that iterates of quasi compact operators converge towards a spectral projection whereas the explicit construction of the limiting operator is in general hard to obtain here we show a simple method to explicitly construct this projection operator provided that the fixed points of the operator and its adjoint are known which is often the case for operators used in approximation theory we use an approach related to riesz schauder and fredholm theory to analyze the iterates of operators on general banach spaces while our main result remains applicable without specific knowledge on the underlying framework applications for markov operators on the space of continuous functions c x are provided where x is a compact hausdorff space

on the spectrum of positive linear operators with a partition of unity property abstract we characterize the spectrum of positive linear operators between banach function spaces having finite rank and a partition of unity property our main result states that all the points in the spectrum are eigenvalues and 1 is the only eigenvalue on the unit circle finally we show that the iterates converge in the uniform operator topology to a projection operator that reproduces constant functions and we provide a simple criterion to obtain the limiting projection operator

on the exact controllability of hyperbolic magnetic schrodinger equations abstract in this paper we address the exact controllability problem for the hyperbolic magnetic schrodinger equation which plays an important role in the research of electromagnetics typical techniques such as hamiltonian induced hilbert spaces and pseudodifferential operators are introduced by choosing an appropriate multiplier we proved the observability inequality with sharp constants in particular a genuine compactness uniqueness argument is applied to obtain the minimal time in the final analysis a suitable boundary control is constructed by the systematic hilbert uniqueness method introduced by j l lions compared with the micro local discussion in bardos et al 1992 we do not require the coefficients belong to c actually c 1 is already sufficient for the vector potential of the hyperbolic electromagnetic equation

spectral conditions for admissibility and observability of wave systems applications to finite element schemes in this article we derive uniform admissibility and observability properties for the finite element space semi discretizations of ddot u a 0 u 0 where a 0 is an unbounded self adjoint positive definite operator with compact resolvent to address this problem we present a new spectral approach based on several spectral criteria for admissibility and observability of such systems our approach provides very general admissibility and observability results for finite element approximation schemes of ddot u a 0 u 0 which stand in any dimension and for any regular mesh in the sense of finite elements our results can be combined with previous works to derive admissibility and observability properties for full discretizations of ddot u a 0 u 0 we also present applications of our results to controllability and stabilization problems

frictional versus viscoelastic damping in a semilinear wave equation in this article we show exponential and polynomial decay rates for the partially viscoelastic nonlinear wave equation subject to a nonlinear and localized frictional damping the equation that models this problem is given by begin eqnarray u tt kappa 0 delta u int 0 t mbox div a x g t s nabla u s ds f u b x h u t 0 mbox in omega times bbb r quad end eqnarray where a b are nonnegative functions a in c 1 overline omega b in l infty omega satisfying the assumption begin eqnarray a x b x geq delta 0 quad forall x in omega end eqnarray and f and h are power like functions we observe that the assumption 0 2 gives us a wide assortment of possibilities from which to choose the functions a x and b x and the most interesting case occurs when one has simultaneous and complementary damping mechanisms taking this point of view into account a distinctive feature of our paper is exactly to consider different and localized damping mechanisms acting in the domain but not necessarily strategically localized dissipations as considered in the prior literature

output feedback stabilization of an unstable wave equation we consider the problem of stabilization of a one dimensional wave equation that contains instability at its free end and control on the opposite end in contrast to classical collocated boundary damper feedbacks for the neutrally stable wave equations with one end satisfying a homogeneous boundary condition the controllers and the associated observers designed in the paper are more complex due to the open loop instability of the plant the controller and observer gains are designed using the method of backstepping which results in explicit formulae for the gain functions we prove exponential stability and the existence and uniqueness of classical solutions for the closed loop system we also derive the explicit compensators in frequency domain the results are illustrated with simulations

a spillover phenomenon in the optimal location of actuators in this paper we are interested in finding the optimal location and shape of the actuators in a stabilization problem namely we consider the one dimensional wave equation damped by an internal feedback supported on a subdomain omega of given length the criterion we want to optimize represents the rate of decay of the total energy of the system it theoretically involves all the eigenmodes of the operator from an engineering point of view it seems more realistic to consider only a finite number of modes say the n first ones in that context we are able to prove existence and uniqueness of an optimal domain omega n it is the better possible location for the actuators we characterize this optimal domain and we point out the following strange phenomenon at least for small lengths the optimal domain omega n which is the better one for the n first modes is actually the worse one for the n 1th mode this looks like the well known spillover phenomenon in control theory at last we will give some possible extension and open problems in higher dimension

controllability of the linear one dimensional wave equation with inner moving forces we address the null inner controllability of the one dimensional wave equation with supports of the controls that may vary with respect to the time variable we consider theoretical and numerical aspects assuming a geometric optic condition on the support of the controls we first prove a generalized observability inequality for the homogeneous wave equation implying the controllability we then introduce and prove the well posedness of a mixed formulation that characterizes the controls of minimal square integrable norm a numerical approximation of this formulation based on a conformal space time finite element method is then presented several numerical experiments are finally reported

distributed source identification for wave equations an offline observer based approach in this paper we consider the 1 d wave equation where the spatial domain is a bounded interval assuming the initial conditions to be known we are here interested in identifying an unknown source term while we take the neumann derivative of the solution on one of the boundaries as the measurement output applying a back and forth iterative scheme and constructing well chosen observers that will be applied in an offline manner we retrieve the source term from the measurement output in the minimal observation time

the asymptotic lift of a completely positive map starting with a unit preserving normal completely positive map l m m acting on a von neumann algebra or more generally a dual operator system we show that there is a unique reversible system n n i e a complete order automorphism of a dual operator system n that captures all of the asymptotic behavior of l called the asymptotic lift of l this provides a noncommutative generalization of the frobenius theorems that describe the asymptotic behavior of the sequence of powers of a stochastic n n matrix in cases where m is a von neumann algebra the asymptotic lift is shown to be a w dynamical system n z and we identify n z as the tail flow of the minimal dilation of l we are also able to identify the poisson boundary of l as the fixed algebra n in general we show the action of the asymptotic lift is trivial iff l is slowly oscillating in the sense that limn ln 1 ln 0 m hence is often a nontrivial automorphism of n the asymptotic lift of a variety of examples is calculated

spectral families of projections in hardy spaces strongly continuous one parameter groups of isometries in the reflexive hardy spaces of the disc d and the half plane are considered in the light of the author s previous joint result with h benzinger and t a gillespie which generalizes stone s theorem for unitary groups to arbitrary banach spaces it is shown that every such group tt of hardy space isometries has a spectral decomposition with respect to a suitable projection valued function on the real line r as in the classical statement of stone s theorem in hilbert space the relevant type of projection valued function is known as a spectral family this circle of ideas is intimately bound up with harmonic analysis particularly in hpr in particular if the group tt acts in hpd and is associated as in forelli s theorem with a group of parabolic mobius transformations of d then it can be analyzed by way of the translation group on hpr the stone type spectral family of the latter is shown to be obtained by restriction of the m riesz projections to hpr by this means a concrete description of the stone type spectral family for a parabolic isometric group on hpd is obtained a pleasant by product of the parabolic case is absorption of the classical paley wiener theorem for hpr 1 p 2 into the framework of the generalized stone s theorem

comparable upper and lower bounds for boundary values of neumann eigenfunctions and tight inclusion of eigenvalues for smooth bounded domains in rn we prove upper and lower l2 bounds on the boundary data of neumann eigenfunctions and we prove quasiorthogonality of this boundary data in a spectral window the bounds are tight in the sense that both are independent of the eigenvalues this is achieved by working with an appropriate norm for boundary functions which includes a spectral weight that is a function of the boundary laplacian this spectral weight is chosen to cancel concentration at the boundary that can happen for whispering gallery type eigenfunctions these bounds are closely related to wave equation estimates due to tataru using this we bound the distance from an arbitrary helmholtz parameter e 0 to the nearest neumann eigenvalue in terms of boundary normal derivative data of a trial function u solving the helmholtz equation e u 0 this inclusion bound improves over previously known bounds by a factor of e5 6 analogously to a recently improved inclusion bound in the dirichlet case due to the first two authors finally we apply our theory to present an improved numerical implementation of the method of particular solutions for computation of neumann eigenpairs on smooth planar domains we show that the new inclusion bound improves the relative accuracy in a computed neumann eigenvalue around the 42000th from nine to fourteen digits with negligible extra numerical effort

theorems of katznelson tzafriri type for contractions for t a contraction on a hilbert space and a function in the disc algebra we show that if 0 on spt then limn t tn 0 the same method gives a new proof of recent results of katznelson tzafriri several applications are given

inverse observability estimates for second order hyperbolic equations with variable coefficients abstract we consider a general second order hyperbolic equation defined on an open bounded domain r n with variable coefficients in both the elliptic principal part and in the first order terms as well at first no boundary conditions b c are imposed our main result theorem 3 5 is a reconstruction or inverse estimate for solutions w under checkable conditions on the coefficients of the principal part the h1 l2 energy at time t t or at time t 0 is dominated by the l2 norms of the boundary traces w a and wt modulo an interior lower order term once homogeneous b c are imposed our results yield under a uniqueness theorem needed to absorb the lower order term continuous observability estimates for both the dirichlet and neumann case with an explicit sharp observability time hence by duality exact controllability results moreover no artificial geometrical conditions are imposed on the controlled part of the boundary in the neumann case in contrast with existing literature the first step of our method employs a riemann geometry approach to reduce the original variable coefficient principal part problem in r n to a problem on an appropriate riemann manifold determined by the coefficients of the principal part where the principal part is the laplacian in our second step we employ explicit carleman estimates at the differential level to take care of the variable first order energy level terms in our third step we employ micro local analysis yielding a sharp trace estimate to remove artificial geometrical conditions on the controlled part of the boundary in the neumann case

stone s theorem for strongly continuous groups of isometries in hardy spaces for 1 p p 2 it is well known that a strongly continuous one parameter group of isometries in the hardy space hp d does not satisfy the classical stone theorem that is there is no additive spectral measure on the borel sets of the real line whose fourier stieltjes transform is the given group however if we relax the topology of hp d by imbedding it into some larger space then it is shown for the case of 1 p 2 that any such group does satisfy stone s theorem when considered as acting in some appropriate larger space the situation for 2 p is more complicated if the group of isometries is of elliptic type then it again satisfies stone s theorem in a suitable larger space however for parabolic groups the situation is fundamentally different such a group can never be interpreted as a fourier stieltjes transform in any space containing hp d

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

theorems of katznelson tzafriri type for semigroups of operators let s be a locally compact abelian semigroup and t a bounded representation of s by linear bounded operators in a banach space x with spectrum sp t let spu t be the intersection of sp t with the set of unitary characters of s we prove that if s r or if t is norm continuous and if f is a function in l1 s which is of spectral synthesis with respect to spu t then inft s sf s t t s ds 0

a generalization of sectorial and quasi sectorial operators abstract in the paper we generalize the main results presented in bentkus and paulauskas 2004 2 by giving rates of approximation of some semigroups of operators of the order n 0 1 also two classes of operators generalizing sectorial and quasi sectorial operators are introduced and their properties are studied

some results of katznelson tzafriri type abstract for semigroups s r z and z k we show that if t is a representation of s by contractions on a hilbert space then inf t s t t f t sup f sp u t s where f l 1 s and sp u t s is the unitary spectrum of t with respect to s for t a representation of a suitable semigroup s by contractions on a banach space we give sharp conditions on sp u t s which guarantee that the equality above holds these conditions concern the thinness of sp u t s in the harmonic analysis sense these results are related to theorems of katznelson tzafriri type which give conditions guaranteeing that inf t s t t f t vanishes

stabilization of the wave equations with potential and indefinite damping by means of global carleman type estimate we study the stabilization problem of the wave equations with potential and indefinite damping the energy decay rate of the system is given explicitly also we obtain an upper bound estimate on the negative damping to guarantee the energy of the system decays exponentially

stability and almost periodicity of trajectories of periodic processes abstract we prove that if the monodromy operator v of a linear periodic process u t in a banach space e is power bounded has countable peripheral spectrum and if its peripheral point spectrum satisfies a certain natural and simple duality condition which always holds in reflexive spaces then every positive trajectory u u 0 x 0 x e is asymptotically almost periodic if in particular the peripheral point spectrum of v is empty then every positive trajectory is asymptotically stable we also obtain results on almost periodicity of complete bounded trajectories and consider conditions under which nontrivial complete trajectories exist

on the exponential decay to equilibrium of the degenerate linear boltzmann equation abstract in this paper we study the decay to the equilibrium state for the solution of the linear boltzmann equation in the torus t d r d z d d n by allowing that the non negative cross section can vanish in a subregion x x t d x 0 of the domain with meas x 0 with respect to the lebesgue measure we show that the geometrical characterization of x is the key property to produce exponential decay to equilibrium

exponential decay of energy of evolution equations with locally distributed damping consider an evolution equation with energy dissipation frac partial partial t y x t ay x t by x t on a bounded x domain omega where by signifies a dissipative perturbation to an otherwise energy conserving system this dissipation may be due to medium impurities viscous effects or artificially imposed dampers and stabilizers it is distributed over only part of the domain omega the question of when the dissipation is effective enough to cause uniform exponential decay of energy is examined because of the locally distributed nature of energy dissipation the problem lacks coercivity and is not directly solvable by energy identities thus to get conditions sufficient for uniform exponential decay a different approach needs to be taken provided here is a set of tight sufficient conditions in terms of the influence of the dissipative operatorbon the separated eigenmodes or clustered eigenmodes ofa the main theorems are general enough to treat the wave and bea

uniform monotonicity of norms and the strong zero two law abstract recently rainer wittmann proved a strong zero two law for positive contractions of lp spaces 1 p

the modulus of a regular linear operator and the zero two law in lp spaces 1 p p 2 abstract using the linear modulus of a regular operator we extend the zero two law for positive contractions of l p spaces 1 p p 2 the proof uses the approximate point spectrum of positive contractions and a procedure obtained by foguel

growth order and stability of discrete semigroups abstract characterizations of the growth order and the stability for the orbit t n x of the powers t n of a bounded linear operator t in terms of cesaro and abel means of the orbit are obtained it is also seen that under the tauberian condition n t n 1 t n o 1 the strong resp uniform convergence of t n is equivalent to its strong resp uniform abel mean convergence

exact controllability of wave equations in rn coupled in parallel abstract we consider a system of two parallel identical wave equations in r n coupled by a distributed internal dissipator it is shown that despite the distributed damping there exists a subspace of states which is unstable we prove an exact controllability result with dirichlet boundary controls with no restrictions on the coupling parameters with a control time that is independent of the coupling constants and dictated by geometric optics

asymptotics for periodic systems abstract this paper investigates the asymptotic behaviour of solutions of periodic evolution equations starting with a general result concerning the quantified asymptotic behaviour of periodic evolution families we go on to consider a special class of dissipative systems arising naturally in applications for this class of systems we analyse in detail the spectral properties of the associated monodromy operator showing in particular that it is a so called ritt operator under a natural resonance condition this allows us to deduce from our general result a precise description of the asymptotic behaviour of the corresponding solutions in particular we present conditions for rational rates of convergence to periodic solutions in the case where the convergence fails to be uniformly exponential we illustrate our general results by applying them to concrete problems including the one dimensional wave equation with periodic damping

tauberian theorems for the laplace stieltjes transform let a 0 oo c be a function of locally bounded variation with a 0 0 whose laplace stieltjes transform g z fo e z da t is absolutely convergent for re z 0 let e be the singular set of g in ir and suppose that 0 e various estimates for lim supt la t g o l are obtained in particular a t g 0 as t oo if i e is null ii sup sup e aysda s oo yee t o o iii lim lim sup sup a s a t 0 610 t oo t 6 s t this result contains tauberian theorems for laplace transforms power series and dirichlet series

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

asymptotic analysis of optimal fixed rate uniform scalar quantization studies the asymptotic characteristics of uniform scalar quantizers that are optimal with respect to mean squared error mse when a symmetric source density with infinite support is sufficiently well behaved the optimal step size spl delta sub n for symmetric uniform scalar quantization decreases as 2 spl sigma n sup 1 v sup 1 1 6n sup 2 where n is the number of quantization levels spl sigma sup 2 is the source variance and v sup 1 spl middot is the inverse of v y y sup 1 spl int sub y sup spl infin p spl sigma sup 1 x x dx equivalently the optimal support length n spl delta sub n increases as 2 spl sigma v sup 1 1 6n sup 2 granular distortion is asymptotically well approximated by spl delta sub n sup 2 12 and the ratio of overload to granular distortion converges to a function of the limit spl tau spl equiv lim sub y spl rarr spl infin y sup 1 e x x y provided as usually happens that spl tau exists when it does its value is related to the number of finite moments of the source density an asymptotic formula for the overall distortion d sub n is obtained and spl tau 1 is both necessary and sufficient for the overall distortion to be asymptotically well approximated by spl delta sub n sup 2 12 applying these results to the class of two sided densities of the form b x sup spl beta e spl alpha x sup spl alpha which includes gaussian laplacian gamma and generalized gaussian it is found that spl tau 1 that spl delta sub n decreases as ln n sup 1 spl alpha n that d sub n is asymptotically well approximated by spl delta sub n sup 2 12 and decreases as ln n sup 2 spl alpha n sup 2 and that more accurate approximations to spl delta sub n are possible the results also apply to densities with one sided infinite support such as rayleigh and weibull and to densities whose tails are asymptotically similar to those previously mentioned

stabilization and control for the nonlinear schrodinger equation on a compact surface in this paper we study the stabilization property and the exact controllability for the nonlinear schrodinger equation on a two dimensional compact riemannian manifold without boundary we use a pseudo differential dissipation the proofs are based on a result of propagation of singularities and on recent dispersion estimates strichartz type inequalities due to n burq p gerard and n tzvetkov

identification of small amplitude perturbations in the electromagnetic parameters from partial dynamic boundary measurements we consider the inverse problem of reconstructing small amplitude perturbations in the conductivity for the wave equation from partial on part of the boundary dynamic boundary measurements through construction of appropriate test functions by a geometrical control method we provide a rigorous derivation of the inverse fourier transform of the perturbations in the conductivity as the leading order of an appropriate averaging of the partial dynamic boundary perturbations this asymptotic formula is generalized to the full time dependent maxwell s equations our formulae may be expected to lead to very effective computational identification algorithms aimed at determining electromagnetic parameters of an object based on partial dynamic boundary measurements

stability of kalman filtering with markovian packet losses we consider kalman filtering in a network with packet losses and use a two state markov chain to describe the normal operating condition of packet delivery and transmission failure based on the sojourn time of each visit to the failure or successful packet reception state we analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance as an estimate of filtering deterioration caused by packet losses which describes the upper envelope of the sequence of error covariance matrices p t t 1 for the case of an unstable scalar model we give sufficient conditions for the stability of the peak covariance process in the general vector case and obtain a sufficient and necessary condition for the scalar case finally the relationship between two different types of stability notions is discussed

wigner measures and observability for the schrodinger equation on the disk we analyse the structure of semiclassical and microlocal wigner measures for solutions to the linear schrodinger equation on the disk with dirichlet boundary conditions our approach links the propagation of singularities beyond geometric optics with the completely integrable nature of the billiard in the disk we prove a structure theorem expressing the restriction of the wigner measures on each invariant torus in terms of second microlocal measures they are obtained by performing a finer localization in phase space around each of these tori at the limit of the uncertainty principle and are shown to propagate according to heisenberg equations on the circle our construction yields as corollaries a that the disintegration of the wigner measures is absolutely continuous in the angular variable which is an expression of the dispersive properties of the equation b an observability inequality saying that the l 2 norm of a solution on any open subset intersecting the boundary resp the l 2 norm of the neumann trace on any nonempty open set of the boundary controls its full l 2 norm resp h 1 norm these results show in particular that the energy of solutions cannot concentrate on periodic trajectories of the billiard flow other than the boundary

admissibility and exact observability of observation operators for micro beam model time and frequency domain approaches this study focuses on the exact observability of a non classical euler bernoulli micro beam equation this non classical model was derived based on the strain gradient elasticity theory which is intended to explain the phenomenon of size effect at the micron scale spectral properties of the corresponding state operator are studied an asymptotic expression for eigenvalues is calculated and eigenfunctions are analyzed in order to check the necessary conditions for the exact observability of the system by examining the eigenfunctions it is shown that among non collocated boundary outputs only measurement of the non classical moment at the root of the beam yields an admissible observation operator and also defines an exactly observable system an alternative proof based on the multiplier method which is commonly employed in the literature on the observability and controllability of infinite dimensional dynamical systems is presented to provide a comparison between the time and frequency domain approaches

exponential stability for infinite dimensional non autonomous port hamiltonian systems abstract we study the non autonomous version of an infinite dimensional linear port hamiltonian system on an interval a b employing abstract results on evolution families we show c 1 well posedness of the corresponding cauchy problem and thereby existence and uniqueness of classical solutions for sufficiently regular initial data further we demonstrate that a dissipation condition in the style of the dissipation condition sufficient for uniform exponential stability in the autonomous case also leads to a uniform exponential decay rate of the energy in this non autonomous setting

power boundedness in fourier and fourier stieltjes algebras and other commutative banach algebras abstract we study power boundedness in the fourier and fourier stieltjes algebras a g and b g of a locally compact group g as well as in some other commutative banach algebras the main results concern the question of when all elements with spectral radius at most one in any of these algebras are power bounded the characterization of power bounded elements in a g and b g and also the structure of the gelfand transform of a single power bounded element

a note on stabilization of locally damped wave equations with time delay abstract in this paper we consider the wave equation with internal distributed time delay and local damping in a bounded and smooth domain r n when the local damping acts on a neighborhood of a suitable part of the boundary of we show that an exponential stability result holds if the coefficient of the delay term is sufficiently small

on power bounded operators abstract the main result asserts that for any contraction t on an arbitrary banach space x t n t n 1 0 as n if and only if the spectrum of t has no points on the unit circle except perhaps z 1 this theorem is extended for t t n where is a function of spectral synthesis on the unit circle as an application we generalize the so called zero two law of ornstein and sucheston and zaharopol to positive contraction on a very large class of banach lattices

almost periodicity of mild solutions of inhomogeneous periodic cauchy problems abstract we consider a mild solution u of a well posed inhomogeneous cauchy problem u t a t u t f t on a banach space x where a is periodic for a problem on r we show that u is asymptotically almost periodic if f is asymptotically almost periodic u is bounded uniformly continuous and totally ergodic and the spectrum of the monodromy operator v contains only countably many points of the unit circle for a problem on r we show that a bounded uniformly continuous solution u is almost periodic if f is almost periodic and various supplementary conditions are satisfied we also show that there is a unique bounded solution subject to certain spectral assumptions on v f and u

kalman filtering with relays over wireless fading channels this note studies the use of relays to improve the performance of kalman filtering over packet dropping links packet reception probabilities are governed by time varying fading channel gains and the sensor and relay transmit powers we consider situations with multiple sensors and relays where each relay can either forward one of the sensors measurements to the gateway fusion center or perform a simple linear network coding operation on some of the sensor measurements using an expected error covariance performance measure we consider optimal and suboptimal methods for finding the best relay configuration and power control problems for optimizing the kalman filter performance our methods show that significant performance gains can be obtained through the use of relays network coding and power control with at least 30 40 less power consumption for a given expected error covariance specification

observability and control of schrodinger equations we propose an exact controllability result for schrodinger equations in bounded domains under the bardos lebeau rauch geometric control condition with an estimate of the control which is explicit with respect to the time of controllability also we prove an explicit in time logarithmic observability estimate for the schrodinger equation where no geometrical conditions are supposed on the domain

tauberian theorems and stability of solutions of the cauchy problem let f r x be a bounded strongly measurable function with values in a banach space x and let ie be the singular set of the laplace transform f in ir suppose that e is countable and 0 e i uf s u du 0 uniformly for s 0 as 0 for each in e it is shown that t 0 e i uf u du f i 0 as t for each in r e in particular f t 0 if f is uniformly continuous this result is similar to a tauberian theorem of arendt and batty it is obtained by applying a result of the authors concerning local stability of bounded semigroups to the translation semigroup on buc r x and it implies several results concerning stability of solutions of cauchy problems

remarks on the asymptotic behavior of the solution to damped wave equations abstract we study the diffusion phenomena for damped wave equations we prove that the solution of an abstract damped wave equation becomes closer to the solution of a heat type equation as time tends to infinity under some assumption to the resolvent as an application of our approach we also study the asymptotic behavior of the damped wave equation in euclidean space under the geometric control condition

asymptotic stability of the wave equation on compact manifolds and locally distributed damping a sharp result let m g be a n dimensional n geqq 2 compact riemannian manifold with boundary where g denotes a riemannian metric of class c this paper is concerned with the study of the wave equation on m g with locally distributed damping described by left begin array l u tt delta bf g u a x g u t 0 quad hbox on thinspace m times left 0 infty right u 0 hbox on partial m times left 0 infty right end array right where m represents the boundary of m and a x g ut is the damping term the main goal of the present manuscript is to generalize our previous result in cavalcanti et al trans ams 361 9 4561 4580 2009 treating the conjecture in a more general setting and extending the result for n dimensional compact riemannian manifolds m g with boundary in two ways i by reducing arbitrarily the region m ast subset m where the dissipative effect lies this gives us a totally sharp result with respect to the boundary measure and interior measure where the damping is effective ii by controlling the existence of subsets on the manifold that can be left without any dissipative mechanism namely a precise part of radially symmetric subsets an analogous result holds for compact riemannian manifolds without boundary

convergence of the wave equation damped on the interior to the one damped on the boundary abstract in this paper we study the convergence of the wave equation with variable internal damping term n x u t to the wave equation with boundary damping x x u t when n x converges to x x in the sense of distributions when the domain in which these equations are defined is an interval in r we show that under natural hypotheses the compact global attractor of the wave equation damped on the interior converges in x h 1 l 2 to the one of the wave equation damped on the boundary and that the dynamics on these attractors are equivalent we also prove in the higher dimensional case that the attractors are lower semicontinuous in x and upper semicontinuous in h 1 e h e

explicit observability inequalities for the wave equation with lower order terms by means of carleman inequalities in this paper by means of carleman estimates and the usual energy estimate we obtain directly two observability inequalities for the linear wave equation with time variant nonsmooth lower order terms we do not need any unique continuation property of the linear equation a priori since this is actually one of the by products of our analysis furthermore the constant in the observability inequality is estimated by an explicit function of the norm of the involved coefficients in the equation also we apply our observability estimates to exact controllability for wave equations

null controllability of a system of linear thermoelasticity we consider a linear system of thermoelasticity in a compact c infin n dimensional connected riemannian manifold this system consists of a wave equation coupled to a heat equation when the boundary of the manifold is non empty dirichlet boundary conditions are considered we study the controllability properties of this system when the control acts in the hyperbolic equation and not in the parabolic one and has its support restricted to an open subset of the manifold we show that if the control time and the support of the control satisfy the geometric control condition for the wave equation this system of thermoelasticity is null controllable more precisely any finite energy solution can be driven to zero at the control time an analogous result is proved when the control acts on the parabolic equation finally when the manifold has no boundary the null controllability of the linear system of three dimensional thermoelastic ity is proved

resolvent conditions and growth of powers of operators abstract following bermudez et al 5 we study the rate of growth of the norms of the powers of a linear operator under various resolvent conditions or cesaro boundedness assumptions in hilbert spaces we prove that if t satisfies the kreiss condition t n o n log n if t is absolutely cesaro bounded t n o n 1 2 e for some e 0 which depends on t if t is strongly kreiss bounded then t n o log n for some 0 we show that a kreiss bounded operator on a reflexive space is abel ergodic and its cesaro means of order converge strongly when 1

fast and strongly localized observation for the schrodinger equation we study the exact observability of systems governed by the schrodinger equation in a rectangle with homogeneous dirichlet respectively neumann boundary conditions and with neumann respectively dirichlet boundary observation generalizing previous results of ramdani takahashi tenenbaum and tucsnak we prove that these systems are exactly observable in arbitrarily small time moreover we show that the above results hold even if the observation regions have arbitrarily small measures more precisely we prove that in the case of homogeneous neumann boundary conditions with dirichlet boundary observation the exact observability property holds for every observation region whith non empty interior in the case of homogeneous dirichlet boundary conditions with neumann boundary observation we show that the exact observability property holds if and only if the observation region has an open intersection with an edge of each direction moreover we give explicit estimates for the blow up rate of the observability constants as the time and or the size of the observation region tend to zero the main ingredients of the proofs are an effective version of a theorem of beurling and kahane on non harmonic fourier series and an estimate for the number of lattice points in the neighbourhood of an ellipse

optimal rates of decay in the katznelson tzafriri theorem for operators on hilbert spaces abstract the katznelson tzafriri theorem is a central result in the asymptotic theory of discrete operator semigroups it states that for a power bounded operator t on a banach space we have t n i t 0 if and only if t t 1 the main result of the present paper gives a sharp estimate for the rate at which this decay occurs for operators on hilbert space assuming the growth of the resolvent norms r e i t as 0 satisfies a mild regularity condition this significantly extends an earlier result by the second author which covered the important case of polynomial resolvent growth we further show that under a natural additional assumption our condition on the resolvent growth is not only sufficient but also necessary for the conclusion of our main result to hold by considering a suitable class of toeplitz operators we show that our theory has natural applications even beyond the setting of normal operators for which we in addition obtain a more general result

logarithmic stability in determining two coefficients in a dissipative wave equation extensions to clamped euler bernoulli beam and heat equations abstract we are concerned with the inverse problem of determining both the potential and the damping coefficient in a dissipative wave equation from boundary measurements we establish stability estimates of logarithmic type when the measurements are given by the operator who maps the initial condition to neumann boundary trace of the solution of the corresponding initial boundary value problem we build a method combining an observability inequality together with a spectral decomposition we also apply this method to a clamped euler bernoulli beam equation finally we indicate how the present approach can be adapted to a heat equation