decay estimates of functions through singular extensions of vector valued laplace transforms abstract let x be a banach space and let f l r x whose laplace transform extends analytically to some region containing i r 0 possibly having a pole at the origin in this paper we give estimates of the decay of certain slight suitable modification of f in terms of the growth of its laplace transform along the imaginary axis this technique is applied to obtain decay estimates of smooth orbits of bounded c 0 semigroups whose infinitesimal generators have an arbitrary finite boundary spectrum these results are close to those given recently by c j k batty and t duyckaerts

the parallel subdomain levelset deflation method in reservoir simulation extreme and isolated eigenvalues are known to be harmful to the convergence of an iterative solver these eigenvalues can be produced by strong heterogeneity in the underlying physics we can improve the quality of the spectrum by deflating the harmful eigenvalues in this work deflation is applied to linear systems in reservoir simulation in particular large sudden differences in the permeability produce extreme eigenvalues the number and magnitude of these eigenvalues is linked to the number and magnitude of the permeability jumps two deflation methods are discussed firstly we state that harmonic ritz eigenvector deflation which computes the deflation vectors from the information produced by the linear solver is unfeasible in modern reservoir simulation due to high costs and lack of parallelism secondly we test a physics based subdomain levelset deflation algorithm that constructs the deflation vectors a priori numerical experiments show that both methods can improve the performance of the linear solver we highlight the fact that subdomain levelset deflation is particularly suitable for a parallel implementation for cases with well defined permeability jumps of a factor 104 or higher parallel physics based deflation has potential in commercial applications in particular the good scalability of parallel subdomain levelset deflation combined with the robust parallel preconditioner for deflated system suggests the use of this method as an alternative for amg

sufficient conditions for conservativity of quantum dynamical semigroups abstract we give sufficient conditions for the conservativity of a quantum dynamical semi group these conditions are expressed as upper bounds of quadratic forms

fast maximum likelihood for blind identification of multiple fir channels this paper develops a fast maximum likelihood method for estimating the impulse responses of multiple fir channels driven by an arbitrary unknown input the resulting method consists of two iterative steps where each step minimizes a quadratic function the two step maximum likelihood tsml method is shown to be high snr efficient i e attaining the cramer rao lower bound crb at high snr the tsml method exploits a novel orthogonal complement matrix of the generalized sylvester matrix simulations show that the tsml method significantly outperforms the cross relation cr method and the subspace ss method and attains the crb over a wide range of snr this paper also studies a fisher information fi matrix to reveal the identifiability of the m channel system a strong connection between the fi based identifiability and the cr based identifiability is established

the stability number of the timoshenko system with second sound abstract in this work we consider the timoshenko beam model with second sound we introduce a new number 0 that characterizes the exponential decay we prove that the corresponding semigroup associated to the system is exponentially stable if and only if 0 0 otherwise there is a lack of exponential stability in this case we prove that the semigroup decays as t 1 2 moreover we show that the rate is optimal

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

the multidimensional wave equation with generalized acoustic boundary conditions i strong stability we study the wave equation on a domain of mathbb r d d geq 2 with dynamical boundary control applied on a part of the boundary and a dirichlet boundary condition on the remaining part we prove the asymptotic stability and nonuniform stability of the associated semigroup

an asymptotic analysis of the fourier laplace transforms of certain oscillatory functions abstract we study the family of fourier laplace transforms f z f p 0 t exp i t i z t d t im z 0 for 1 and c where hadamard finite part is used to regularize the integral when re 1 we prove that each f has analytic continuation to the whole complex plane and determine its asymptotics along any line through the origin we also apply our ideas to show that some of these functions provide concrete extremal examples for the wiener ikehara theorem and a quantified version of the ingham karamata theorem supplying new simple and constructive proofs of optimality results for these complex tauberian theorems

decay of solutions for a mixture of thermoelastic one dimensional solids we study a pde system modeling thermomechanical deformations for a mixture of thermoelastic solids in particular we investigate the asymptotic behavior of the solutions first we identify conditions on the constitutive coefficients to guarantee that the imaginary axis is contained in the resolvent subsequently we find the necessary and sufficient conditions to guarantee the exponential decay of solutions when the decay is not of exponential type we prove that the solutions decay polynomially and we find the optimal polynomial decay rate

resolvent estimates in homogenisation of periodic problems of fractional elasticity we provide operator norm convergence estimates for solutions to a time dependent equation of fractional elasticity in one spatial dimension with rapidly oscillating coefficients that represent the material properties of a viscoelastic composite medium assuming periodicity in the coefficients we prove operator norm convergence estimates for an operator fibre decomposition obtained by applying to the original fractional elasticity problem the fourier laplace transform in time and gelfand transform in space we obtain estimates on each fibre that are uniform in the quasimomentum of the decomposition and in the period of oscillations of the coefficients as well as quadratic with respect to the spectral variable on the basis of these uniform estimates we derive operator norm type convergence estimates for the original fractional elasticity problem for a class of sufficiently smooth densities of applied forces

on line blind multichannel equalization based on mutually referenced filters this paper presents a novel approach to the blind linear equalization of possibly nonminimum phase and time varying communication channels in the context of channel diversity we introduce the concept of mutually referenced equalizers mres in which several filters are considered the outputs of which act as training signals for each other a corresponding constrained multidimensional mean square error mse cost function is derived the minimization of which is shown to be a necessary and sufficient condition for equalization the links with a standard linear prediction problem are demonstrated the proposed technique exhibits properties of important practical concern 1 the proposed algorithm is globally convergent 2 simple closed form solutions exist for the mres but the mres also lend themselves readily to adaptive implementation in particular the recursive least squares rls algorithm can be used to offer optimal convergence rate 3 the mre method provides a solution for all equalization delays which results in robustness properties with respect to snr and ill defined channel lengths

on timoshenko type systems with type iii thermoelasticity asymptotic behavior abstract in this study we consider a thermoelastic beam system where the oscillations are defined by the timoshenko model and heat conduction is given by the green and naghdi theories we provide an explicit characterization of the decay rate which can be exponential or polynomial depending on the relationship between the coefficients of the wave propagation speed

the lack of exponential stability in certain transmission problems with localized kelvin voigt dissipation in this paper we consider the transmission problem of a material composed of three components one of them is a kelvin voigt viscoelastic material the second is an elastic material no dissipation and the third is an elastic material inserted with a frictional damping mechanism the main result of this paper is that the rate of decay will depend on the position of each component when the viscoelastic component is not in the middle of the material then there exists exponential stability of the solution instead when the viscoelastic part is in the middle of the material there is not exponential stability in this case we show that the corresponding solution decays polynomially as 1 t 2 moreover we show that the rate of decay is optimal over the domain of the infinitesimal generator finally using a second order scheme that ensures the decay of energy newmark beta method we give some numerical examples which demonstrate this asymptotic behavior

direct integrals of strongly continuous operator semigroups abstract the goal of this article is to develop a theory for direct integrals of c 0 semigroups on hilbert spaces parallel to the recent approach by lachowicz and moszynski for direct sums of banach spaces diagonal operators and semigroups in it we deal with the existence and characterisation of semigroups asymptotic rates and questions of decomposability

adaptive step size algorithms for blind interference suppression in ds cdma systems this paper develops adaptive step size blind lms algorithms and adaptive forgetting factor blind rls algorithms for code aided suppression of multiple access interference mai and narrowband interference nbi in ds cdma systems these algorithms optimally adapt both the step size forgetting factor and the weight vector of the blind linear multiuser detector using the received measurements simulations are provided to compare the proposed algorithms with previously studied blind rls and blind lms algorithms they show that the adaptive step size blind lms algorithm and adaptive forgetting factor blind rls algorithm field significant improvements over the standard blind lms algorithm and blind rls algorithm in dynamic environments where the number of interferers are time varying

decay rates for 1 d mixed type ii and type iii thermoelastic system with localized viscous damping abstract this work is devoted to discussing that how the locations of the thermal and viscous damping affect the stability of the 1 d elastic systems the spatial domain of the 1 d thermoelastic system under consideration can be divided into three sub intervals that is the thermoelastic region of type ii the one of type ii with viscous damping and the one of type iii the following two kinds of energy decay rates for the system are obtained 1 if the thermoelastic region of type iii includes one exterior point of the spatial domain of the system the energy of the system decays exponentially 2 if not that is the thermoelastic region of type iii is strictly inside the spatial domain the system always lacks of exponential decay however the optimal polynomial decay rate is further estimated for this system with smooth initial states finally some numerical simulations are presented to verify the stability results obtained in this work

on the use of rigid body modes in the deflated preconditioned conjugate gradient method large discontinuities in material properties such as those encountered in composite materials lead to ill conditioned systems of linear equations these discontinuities give rise to small eigenvalues that may negatively affect the convergence of iterative solution methods such as the preconditioned conjugate gradient method this paper considers the deflated preconditioned conjugate gradient method for solving such systems our deflation technique uses as the deflation space the rigid body modes of sets of elements with homogeneous material properties we show that in the deflated spectrum the small eigenvalues are mapped to zero and no longer negatively affect the convergence we justify our approach through mathematical analysis and show with numerical experiments on both academic and realistic test problems that the convergence of our dpcg method is independent of discontinuities in the material properties

on channel identification based on second order cyclic spectra gardener 1991 presented an interesting use of cyclostationarity for channel identification in pam data communication systems the present paper presents new results that address the identification of linear rational channels with higher than minimum bandwidth based on the use of second order cyclic statistics unlike the approach taken by gardener the present authors show that channel identification is achievable for a class of linear channels without the need for a pilot tone or training periods moreover channel identification based on cyclic statistics does not preclude gaussian or near gaussian inputs

optimal rates of decay for operator semigroups on hilbert spaces abstract we investigate rates of decay for c 0 semigroups on hilbert spaces under assumptions on the resolvent growth of the semigroup generator our main results show that one obtains the best possible estimate on the rate of decay that is to say an upper bound which is also known to be a lower bound under a comparatively mild assumption on the growth behaviour this extends several statements obtained by batty et al 2016 6 in fact for a large class of semigroups our condition is not only sufficient but also necessary for this optimal estimate to hold even without this assumption we obtain a new quantified asymptotic result which in many cases of interest gives a sharper estimate for the rate of decay than was previously available and for semigroups of normal operators we are able to describe the asymptotic behaviour exactly we illustrate the strength of our theoretical results by using them to obtain sharp estimates on the rate of energy decay for a wave equation subject to viscoelastic damping at the boundary

b convexity the analytic radon nikodym property and individual stability ofc0 semigroups abstract lett t t t 0be ac0 semigroup on a banach spacex with generatoraand growth bound assume thatx0 xis such that the local resolvent r a x0admits a bounded holomorphic extension to the right half plane re 0 we prove the following results i ifhas fourier type 1 2 then lim 0 for all 1 and ii ifhas the analytic rnp then lim 0 for all 1 and iii ifis arbitrary then weak lim 0 for all 1 and as an application we prove a tauberian theorem for the laplace transform of functions with values in ab convex banach space

a coarse space for heterogeneous helmholtz problems based on the dirichlet to neumann operator the helmholtz equation governing wave propagation and scattering phenomena is difficult to solve numerically its discretization with piecewise linear finite elements results in typically large linear systems of equations the inherently parallel domain decomposition methods constitute hence a promising class of preconditioners an essential element of these methods is a good coarse space here the helmholtz equation presents a particular challenge as even slight deviations from the optimal choice can be devastating in this paper we present a coarse space that is based on local eigenproblems involving the dirichlet to neumann operator our construction is completely automatic ensuring good convergence rates without the need for parameter tuning moreover it naturally respects local variations in the wave number and is hence suited also for heterogeneous helmholtz problems the resulting method is parallel by design and its efficiency is demonstrated on 2d homogeneous and heterogeneous numerical examples

optimal energy decay in a one dimensional wave heat system with infinite heat part abstract using recent results in the theory of c 0 semigroups due to batty et al 2016 5 we study energy decay in a one dimensional coupled wave heat system with finite wave part and infinite heat part our main result provides a sharp estimate for the rate of energy decay of a certain class of classical solutions the present paper can be thought of as a natural sequel to a recent work by batty et al 2016 6 which studied a similar wave heat system with finite wave and heat parts using a celebrated result due to borichev and tomilov

stabilization of non homogeneous elastic materials with voids we study the asymptotic behavior of the solution of the non homogeneous elastic system with voids and a thermal effect we first prove the well posedness of this system under some realistic assumptions on the coefficients since this system suffers of exponential stability as shown in dimension 1 in pamplona munoz rivera and quintanilla 2009 18 our main results concern strong and polynomial stabilities again under some assumptions on the coefficients these stabilities are obtained in a closed subspace of the natural hilbert space hence we characterize its orthogonal and further show that in the whole space the energy tends strongly or polynomially to the energy of the projection of the initial datum on this orthogonal space in this respect we extend and precise former results obtained in one dimension in pamplona munoz rivera and quintanilla 2009 18

on the structure of covariant dynamical semigroups abstract dynamical semigroups in b h without the norm continuity assumption are investigated by introducing the notion of form generator giving the mathematical expression for the idea of markovian master equation it is shown that any form generator on b h admits a standard representation and the non uniqueness of this representation is described the equations for the components of the standard representation of a covariant form generator are deduced in terms of low order cohomology of the symmetry group in particular noncommutative levy khinchin type formulae for the shift covariant form generators are obtained relations with previous works on characterisation of the unbounded generator of a dynamical semigroup are discussed

on reduction theory and brown measure for closed unbounded operators abstract the theory of direct integral decompositions of both bounded and unbounded operators is further developed in particular results about spectral projections functional calculus and affiliation to von neumann algebras are proved for operators belonging to or affiliated to a tracial von neumann algebra that is a direct integral von neumann algebra the brown measure is shown to be given by the corresponding integral of brown measures

a least squares approach to blind channel identification conventional blind channel identification algorithms are based on channel outputs and knowledge of the probabilistic model of channel input in some practical applications however the input statistical model may not be known or there may not be sufficient data to obtain accurate enough estimates of certain statistics in this paper we consider the system input to be an unknown deterministic signal and study the problem of blind identification of multichannel fir systems without requiring the knowledge of the input statistical model a new blind identification algorithm based solely on the system outputs is proposed necessary and sufficient identifiability conditions in terms of the multichannel systems and the deterministic input signal are also presented

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

polynomial stability of the rao nakra beam with a single internal viscous damping abstract in this paper we consider the stability of the rao nakra sandwich beam equation with various boundary conditions which consists of two wave equations for the longitudinal displacements of the top and bottom layers and one euler bernoulli beam equation for the transversal displacement polynomial stability of certain orders are obtained when there is only one viscous damping acting either on the beam equation or one of the wave equations for a few special cases optimal orders are confirmed we also study the synchronization of the model with viscous damping on the transversal displacement our results reveal that the order of the polynomial decay rate is sensitive to various boundary conditions and to the damping locations

frequency domain approach for the polynomial stability of a system of partially damped wave equations in this paper we study the stability of a system of wave equations which are weakly coupled and partially damped using a frequency domain approach based on the growth of the resolvent on the imaginary axis we establish the polynomial energy decay rate for smooth initial data we show that the behavior of the system is sensitive to the arithmetic property of the ratio of the wave propagation speeds of the two equations

polynomial stability of the timoshenko system by one boundary damping abstract in this paper we study the indirect boundary stabilization of the timoshenko system with only one dissipation law this system which models the dynamics of a beam is a hyperbolic system with two wave speeds assuming that the wave speeds are equal we prove non uniform stability and an optimal polynomial energy decay rate is obtained otherwise if the ratio of the wave speeds is a rational number we show that the decay rate is of polynomial type

operators l1 r x and the norm continuity problem for semigroups we present a new method for constructing c0 semigroups for which properties of the resolvent of the generator and continuity properties of the semigroup in the operator norm topology are controlled simultaneously it allows us to show that a there exists a c0 semigroup which is continuous in the operator norm topology for no t 0 1 such that the resolvent of its generator has a logarithmic decay at infinity along vertical lines b there exists a c0 semigroup which is continuous in the operator norm topology for no t r such that the resolvent of its generator has a decay along vertical lines arbitrarily close to a logarithmic one these examples rule out any possibility of characterizing norm continuity of semigroups on arbitrary banach spaces in terms of resolvent norm decay on vertical lines

blind channel identification via stochastic approximation constant step size algorithms this work is devoted to the study of a class of recursive algorithms for blind channel identification using weak convergence methods the convergence of the algorithm is obtained and the rate of convergence is ascertained the technique discussed can also be used in the analysis of rates of convergence for decreasing step size algorithms

optimal polynomial decay of functions and operator semigroups we characterize the polynomial decay of orbits of hilbert space c 0 semigroups in resolvent terms we also show that results of the same type for general banach space semigroups and functions obtained recently in batty and duyckaerts j evol eq 8 765 780 2008 are sharp this settles a conjecture posed in batty and duyckaerts 2008

stabilization of a joint leg beam system with boundary damping abstract in this paper we study a model for combined axial and transverse motions of two euler bernoulli beams connected through two legs to a joint we prove that the joint leg beam system is polynomially stable but not exponentially stable with linear control of velocity feedback

a study on damping rates and boundary feedback control in distributed parameter vibrating systems abstract the study of damping rates for distributed and boundary feedback control systems is important in the design of control mechanisms for distributed parameter systems despite the fact that many papers have been published regarding the determination of spectra and also possibly the sharpest systemwide uniform rates of energy decay many problems remain open in this paper we first mention a few examples of distributed and boundary damping then proceed to examine the simplest such possible case of boundary feedback control of the one dimensional wave equation using the wave propagation method one can see that the analysis of the spectra is quite sophisticated indeed for most cases with seemingly the best efforts one can only pin down the rates of damping in some narrow range several open questions are posed at the end of the paper which along with higher dimensional problems we hope will further motivate more studies in such decay spectral analysis

characteristic conditions of the generation of c0 semigroups in a hilbert space abstract in this paper new characteristic conditions in terms of a and the first order resolvent of a and a which assure that a generates a c 0 semigroup in a hilbert space are proposed and proved the conditions can be used to investigate the well posedness problem of non dissipative systems an example is also given to show how to use them

indirect stabilization of weakly coupled kirchhoff plate and wave equations with frictional damping abstract we investigate the indirect stabilization of a weakly coupled system consisting of a kirchhoff plate equation involving free boundary conditions and the wave equation with dirichlet boundary conditions in a bounded domain the distributed damping is frictional and appears in one of the equations only first we consider the case where the damping occurs in the wave equation and using the frequency domain method combined with an interpolation inequality we derive a polynomial decay estimate for the associated semigroup afterwards we consider the case where the frictional damping occurs in the kirchhoff plate equation and we use the same technique to derive a polynomial decay estimate for the underlying semigroup that latter polynomial decay estimate is similar to the one obtained earlier by different authors in the case of a coupling between a frictionally damped euler bernoulli plate equation and an undamped wave equation which is quite surprising since the operator defining the damping in the kirchhoff plate equation is compact

generators of quantum markov semigroups quantum markov semigroups qmss originally arose in the study of the evolutions of irreversible open quantum systems mathematically they are a generalization of classical markov semigroups where the underlying function space is replaced by a non commutative operator algebra in the case when the qms is uniformly continuous theorems due to the works of lindblad commun math phys 48 119 130 1976 stinespring proc am math soc 6 211 216 1955 and kraus ann phys 64 311 335 1970 imply that the generator of the semigroup has the form l a n 1 vn avn ga ag where vn and g are elements of the underlying operator algebra in the present paper we investigate the form of the generators of qmss which are not necessarily uniformly continuous and act on the bounded operators of a hilbert space we prove that the generators of such semigroups have forms that reflect the results of lindblad and stinespring we also make some progress towards forms reflecting kraus result finally we look at