intrinsic ultracontractivity and small perturbation for one dimensional generalized diffusion operators abstract we consider a one dimensional generalized diffusion operator g on an open interval which is not necessarily bounded we characterize sp i e 1 is a small perturbation of the operator g in terms of the classification of the boundary points from the view point of diffusion processes and give a sufficient condition for iu i e the associated heat kernel is intrinsically ultracontractive

conditional scores and optimal scores for generalized linear measurement error models abstract this paper studies estimation of the parameters of generalized linear models in canonical form when the explanatory vector is measured with independent normal error for the functional case i e when the explanatory vectors are fixed constants unbiased score functions are obtained by conditioning on certain sufficient statistics this work generalizes results obtained for logistic regression in the case that the explanatory vectors are independent and identically distributed with unknown distribtuion efficient score functions are obtained using the theory developed in begun et al 1983 keywords conditional score function efficient score function functional model generalized linear model measurement error structural model

gaussian heat kernel upper bounds via the phragmen lindelof theorem we prove that in presence of l gaussian estimates so called davies gaffney estimates on diagonal upper bounds imply precise off diagonal gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces

a two stage filter for smoothing multivariate noisy data on unstructured grids abstract experimental data as well as numerical simulations are very often affected by noise random fluctuations that distort the final output or the intermediate products of a numerical process in this paper a new method for smoothing data given on nonstructured grids is proposed it takes advantage of the smoothing properties of kernel weighted averaging and least squares techniques the weighted averaging is performed following a shepard like procedure where gaussian kernels are employed while least squares fitting is reduced to the use of very few basis functions so as to improve smoothness though at the price of interpolation accuracy once we have defined an n point grid and want to make a smoothed fit at a given grid point this method reduces to consideration of all m point stencils for a given value of m where m n that include that point and to make a least squares fitting for that particular point in each of those stencils finally the various results thus obtained are weight averaged the weights being inversely proportional to the distance of the point to the middle of the stencil then this process is repeated for all the grid points so as to obtain the smoothing of the input function though this method is generalized for the multivariate case one two and five dimensional test cases are shown as examples of the performance of this method

a spectral multiplier theorem for a sublaplacian on su 2 we prove a hormander type spectral multiplier theorem for a sublaplacian on su 2 with critical index determined by the euclidean dimension of the group this result is the analogue for su 2 of the result for the heisenberg group obtained by d muller and e m stein and by w hebisch

on the toda and kac van moerbeke systems given a solution of the toda lattice we explicitly construct a solution of the kac van moerbeke system related to each other by a miura type transformation as an illustration of our method we derive the n soliton solutions of the kac van moerbeke lattice

structure and stability of finite dimensional approximations for functional differential equations this paper deals with the structural and stability properties of the averaging approximation scheme for linear retarded functional differential equations both in the discrete and in the continuous time case the structure of the approximating systems is shown to be analogous to the structure of the underlying retarded equation moreover it is shown that the approximating systems are exponentially stable in a uniform sense if the original system is asymptotically stable

critical phenomena in linear elliptic problems abstract in this article we consider the existence and nonexistence of principal eigenvalues for the linear elliptic equation u v x u in r n and u d 1 2 r n where n 3 and v l 1 loc r n with v 0 in r n we establish that when potential v has strong singularities phenomena which appear under critical exponent nonlinearities brezis and nirenberg are present in linear problems as well

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

dispersive estimates for rational symbols and local well posedness of the nonzero energy nv equation abstract we consider the cauchy problem for the two dimensional novikov veselov equation integrable via the inverse scattering problem for the schrodinger operator with fixed negative energy the associated linear equation is characterized by a rational symbol which is not a polynomial except when the energy parameter is zero with the help of a complex analysis point of view of the problem we establish uniform decay estimates for the linear solution with gain of almost one derivative and we use this result together with fourier decomposition methods and x s b spaces to prove local well posedness in h s s 1 2

on the efficient low cost procedure for estimation of high dimensional prediction error covariance matrices abstract a simple efficient algorithm is proposed for estimating the prediction error covariance matrix which plays the key role for successful state estimation in very high dimensional systems the main results are obtained by introducing the hypothesis on the separability of vertical and horizontal structure of the error covariance matrix and its parameterization a new parameter optimization problem is formulated which is closely related to the nearest kronecker problem nkp this allows to estimate optimally the unknown parameters of the structured parametrized ecm as well as to approach numerically the solution of the traditional nkp in a simple and efficient way the algorithm for the state estimation will be detailed the results from experiments on parameter and state estimation problems for both moderate and high dimensional numerical models demonstrate a high effectiveness of the proposed filtering approach

trudinger moser inequality with remainder terms abstract the paper gives the following improvement of the trudinger moser inequality 0 1 sup u 2 d x u 1 u c 0 e 4 u 2 d x r 2 related to the hardy sobolev mazya inequality in higher dimensions we show 0 1 with u v x u 2 d x for a class of v 0 that includes v r 1 4 r 2 log 1 r 2 max log 1 r 1 which refines two previously known cases of 0 1 proved by adimurthi and druet 2 and by wang and ye 23 in addition we verify 0 1 for u u p 2 as well as give an analogous improvement for the onofri beckner inequality for the unit disk beckner 6

positive harmonic functions on complete manifolds of negative curvature this paper studies the interaction between the geometry of complete riemannian manifolds of negative curvature and some aspects of function theory on these spaces the study of harmonic functions on the unit disc provides a classical and beautiful example of this interaction we recall some aspects of this below there is a well known representation of positive harmonic functions on the unit disc u due to herglotz 13 in terms of positive borel measures tt on the circle s1

approximation schemes for the linear quadratic optimal control problem associated with delay equations the linear regulator problem for delay equations is discussed we propose a theoretical solution involving riccati integral equations and then axiomatically discuss a general approximation scheme the details are given for spline and averaging approximations

convergence properties of the riccati difference equation in optimal filtering of nonstabilizable systems this paper studies the convergence and properties of the solutions of the riccati difference equation special emphasis is given to systems which are not necessarily stabilizable in the filtering sense particularly those having uncontrollable roots on the unit circle besides generalizing and unifying previous work the results have application to a number of important problems including filtering and control of systems with purely deterministic disturbances such as sinusoids and drift components

commutation methods applied to the mkdv equation an explicit construction of solutions of the modified korteweg de vries equation given a solution of the ordinary korteweg de vries equation is provided our theory is based on commutation methods i e n 1 supersymmetry underlying miura s transformation that links solutions of the two evolution equations

subcriticality and gaugeability of the schrodinger operator we investigate a schrodinger operator 2 v in r d d 3 with a potential v in the class k d satisfying a similar kato condition at infinity and prove an equivalence theorem connecting various conditions on subcriticality strong positivity and gaugeability of the operator

lp norms of non critical schrodinger semigroups we consider schrodinger semigroups e th h v on rn with v c x 2 as x 0 c 12 n 2 2 with h 0 we determine the exact power law divergence of e th p p and of some e th q p as maps from lp to lq the results are expressed most naturally in terms of the power for which there exists a positive resonance such that h 0 x x

on the design of a stable adaptive filter for state estimation in high dimensional systems design of specific parametrized gain structures provides a new tool for ensuring stability of reduced order filter for high dimensional systems which is optimized adaptively in the minimum prediction error framework

approximate quasi likelihood estimation in models with surrogate predictors abstract we consider quasi likelihood estimation with estimated parameters in the variance function when some of the predictors are measured with error we review and extend four approaches to estimation in this problem all of them based on small measurement error approximations a taxonomy of the data sets likely to be available in measurement error studies is developed an asymptotic theory based on this taxonomy is obtained and includes measurement error and berkson error models as special cases

methodology for non parametric deconvolution when the error distribution is unknown summary in the non parametric deconvolution problem to estimate consistently a density or distribution from a sample of data contaminated by additive random noise it is often assumed that the noise distribution is completely known or that an additional sample of replicated or validation data is available methods also have been suggested for estimating the scale of the error distribution but they require somewhat restrictive smoothness assumptions on the signal distribution which can be difficult to verify in practice we take a completely new approach to the problem not requiring extra data of any type we argue that data rarely come from a simple regular distribution and that this can be exploited to estimate the signal distributions by using a simple procedure our method can be extended to other problems involving errors in variables such as non parametric regression estimation its performance in practice is remarkably good often equalling even unexpectedly the performance of techniques that use additional data to estimate the unknown error distribution

critical dissipative estimate for a heat semigroup with a quadratic singular potential and critical exponent for nonlinear heat equations abstract we consider a heat semigroup with an inverse square potential and prove critical dissipative estimates including the endpoint case some application to a nonlinear heat equation with an inverse square potential is also discussed

on the upper estimate of the heat kernel of a complete riemannian manifold let m be a complete non compact riemannian manifold whose sectional curvature is bounded between two constants k and k then one expects that the heat diffusion in such a manifold behaves like the heat diffusion in euclidean space the purpose of this paper is to give a justification of such a statement in 5 j cheeger and the third author found a lower estimate of the heat kernel by comparing it with the heat kernel of the space form whose curvature is the lower bound of the curvature of the manifold this lower estimate is sharp if we insist the dependence should be on the lower bound of the ricci curvature alone it remains to give an upper estimate of the heat kernel one does not however expect to have a comparison theorem for the upper bound because it is more sensitive to the geometry of the manifold in fact the heat kernel of the upper hialf space and the heat kernel of the complete hyperbolic manifold with finite volume have quite different behavior this is reflected by the fact that the laplacian has no discrete spectrum in the first case while infinite number of discrete eigenvalues may exist in the latter case what we will prove here is that in any case the heat kernel has to decay in a manner similar to the euclidean heat kernel thus we will prove that for any constant c 4 there exists c1 depending on c t the bound of the curvature of m and x so that for all t e 0 t

a new reduced order adaptive filter for state estimation in high dimensional systems a simple reduced order adaptive filter optimal in the sense of minimum prediction error is proposed for estimating the state of high dimensional systems in which the process and observation noise statistics are unknown it is shown that implementation of this adaptive filter requires the solution of only two linear difference equations the dimensions of which are the dimensions of the full and reduced states respectively and that no solution of either an algebraic riccati equation or a lyapunov equation is needed in addition substantial gain in computer memory and cpu time is obtained by parametrization of the filter gain in the form of the product of two matrices one of which is a prescribed projection from the reduced space onto the full space a twin experiment on data assimilation with a quasi geostrophic ocean model shows the efficiency of the proposed approach

schrodinger equations with critical nonlinearity singular potential and a ground state we study semilinear elliptic equations in a generally unbounded domain rn when the pertinent quadratic form is nonnegative and the potential is generally singular typically a homogeneous function of degree 2 we prove solvability results based on the asymptotic behavior of the potential with respect to unbounded translations and dilations while the nonlinearity is a perturbation of a self similar possibly oscillating term f of critical growth satisfying f js n 2n 2jf s j z s r this paper focuses on two qualitatively different cases of this problem one when the quadratic form has a generalized ground state and another where the presence of potential does not change the energy space in the latter case we allow nonlinearities with oscillatory critical growth an important example of such quadratic form is the one on rn with the radial hardy potential x 2 with in the first case in the second case where n 2 24 is the largest constant for which the energy form remains nonnegative

sharp decay estimates of lq norms for nonnegative schrodinger heat semigroups abstract let h v be a nonnegative schrodinger operator on l 2 r n where n 3 and v is a radially symmetric nonpositive function in r n decaying quadratically at the space infinity for any 1 p q we denote by e t h q p the operator norm of the schrodinger heat semigroup e t h from l p r n to l q r n in this paper under suitable conditions on v we give the exact and optimal decay rates of e t h q p as t for all 1 p q the decay rates of e t h q p depend on whether the operator h is subcritical or critical and on the behavior of the positive harmonic function for the operator h

martin compactification of a complete surface with negative curvature in this paper we consider the martin compactification associated with the operator mathcal l delta 1 of a complete non compact surface sigma 2 with negative curvature in particular we investigate positive eigenfunctions with eigenvalue one of the laplace operator delta of sigma 2 and prove a uniqueness result such eigenfunctions are unique up to a positive multiplicative constant if they vanish on the part of the geometric boundary s infty sigma 2 of sigma 2 where the curvature is bounded above by a negative constant and satisfy some growth estimate on the other part of s infty sigma 2 where the curvature approaches zero this uniqueness result plays an essential role in our recent paper cao and he infinitesimal rigidity of steady gradient ricci soliton in dimension three arxiv 1412 2714 2014 preprint in which we prove an infinitesimal rigidity theorem for deformations of certain three dimensional collapsed gradient steady ricci soliton with a non trivial killing vector field

lp norms of nonnegative schrodinger heat semigroup and the large time behavior of hot spots this paper is concerned with the cauchy problem for the heat equation with a potential p tu u v x uin rn 0 u x 0 x in rn where t t n 3 l2 rn and v v x is a smooth nonpositive and radially symmetric function having quadratic decay at the space infinity in this paper we assume that the schrodinger operator h v is nonnegative on l2 rn and give the exact power decay rates of lq norm q 2 of the solution e th of p as t furthermore we study the large time behavior of the solution of p and its hot spots

positive solutions and large time behaviors of schrodinger semigroups simon s problem let h v where v is a multiplication operator by a real valued function v x on rn which is uniformly holder continuous and 1 x 2 2 v x l rn for some 4 the relationship between existence of positive solutions with growth conditions of hg 0 and asymptotic behaviors as t of e th is established using it b simon s problem for h on r2 is solved

martin boundaries of elliptic skew products semismall perturbations and fundamental solutions of parabolic equations abstract we consider positive solutions of elliptic partial differential equations on non compact domains of riemannian manifolds we explicitly determine martin boundaries and martin kernels for a class of elliptic equations in skew product form by exploiting and developing perturbation theory for elliptic equations and short long time estimates for fundamental solutions of parabolic equations

spectral multipliers via resolvent type estimates on non homogeneous metric measure spaces we describe a simple but surprisingly effective technique of obtaining spectral multiplier results for abstract operators which satisfy the finite propagation speed property for the corresponding wave equation propagator we show that in this setting spectral multipliers follow from resolvent or semigroup type estimates the most notable point of the paper is that our approach is very flexible and can be applied even if the corresponding ambient space does not satisfy the doubling condition or if the semigroup generated by an operator is not uniformly bounded as a corollary we obtain l p spectrum independence for several second order differential operators and recover some known results our examples include the laplace belltrami operator on manifolds with ends and schrodinger operators with strongly subcritical potentials

constructing solutions of the mkdv equation abstract using commutation methods i e n 1 supersymmetry underlying miura s transformation an explicit construction of solutions of the modified korteweg de vries equation given a solution of the ordinary korteweg de vries equation is provided

controller reduction concepts and approaches the problem of passing from a linear time invariant high order controller designed for a linear time invariant plant of presumably high order to a low order approximation of the controller is discussed the approximation problem is often best posed as a frequency weighted l sub infinity approximation problem many different controller representations are possible giving different performances of the various reduction algorithms

on schrodinger operators with multipolar inverse square potentials abstract positivity essential self adjointness and spectral properties of a class of schrodinger operators with multipolar inverse square potentials are discussed in particular a necessary and sufficient condition on the masses of singularities for the existence of at least a configuration of poles ensuring the positivity of the associated quadratic form is established

lp spectral theory of kleinian groups let be a geometrically finite group acting on the hyperbolic space hn 1 and let h denote the laplace beltrami operator on m hn 1 which we assume is not compact if m is either of finite volume or cusp free we determine completely the lp spectrum of h for 1 p finding that it depends upon p in a nontrivial manner we also obtain a number of pointwise and lp decay properties of the l2 eigenfunctions associated with eigenvalues e in the range 0 e n24

the heat kernel of a schrodinger operator with inverse square potential we consider the schrodinger operator h v x with radial potential v which may have singularity at 0 and a quadratic decay at infinity first we study the structure of positive harmonic functions of h and give their precise behavior second under quite general conditions we prove an upper bound for the correspond heat kernel p x y t of the type 0 p x y t ct n 2u min x t u min y t u t 2exp x y 2ct for all x y rn and t 0 where u is a positive harmonic function of h third if u2 is an a2 weight on rn then we prove a lower bound of a similar type

riesz transform gaussian bounds and the method of wave equation for an abstract self adjoint operator l and a local operator a we study the boundedness of the riesz transform al on lp for some 0 a very simple proof of the obtained result is based on the finite speed propagation property for the solution of the corresponding wave equation we also discuss the relation between the gaussian bounds and the finite speed propagation property using the wave equation methods we obtain a new natural form of the gaussian bounds for the heat kernels for a large class of the generating operators we describe a surprisingly elementary proof of the finite speed propagation property in a more general setting than it is usually considered in the literature

prediction error sampling procedure based on dominant schur decomposition application to state estimation in high dimensional oceanic model abstract iterative procedure is described to generate patterns of dominant schur vectors of the system dynamics their roles in estimating the filter gain is study these patterns are produced by several integrations of the model from a set of perturbations this approach is motivated by a number of interesting results on stability of the filter whose gain is approximated in a subspace of dominant schur vectors a simple method for the filter design is presented which is aimed at overcoming the most serious drawback of advanced filtering algorithms for high dimensional systems related to very high computational cost in evaluation of the filter gain the resulting filter will be compared with the existing ones showing its relevance from a practical point of view in order to demonstrate its efficiency the new filter is tested on various experiments these experiments include the much studied problem of estimating the solution of the lorenz system as well as that of assimilating sea surface height observations in a high dimensional oceanic model it is shown that significant increases in efficiency can be obtained by using this filter and that the proposed filter is very promising for solving realistic assimilation problems in meteorology and oceanography

sharp two sided heat kernel estimates of twisted tubes and applications we prove on diagonal bounds for the heat kernel of the dirichlet laplacian delta d omega in locally twisted three dimensional tubes in particular we show that for any fixed x the heat kernel decays for large times as rm e e 1t t 3 2 where e1 is the fundamental eigenvalue of the dirichlet laplacian on the cross section of the tube this shows that any suitably regular local twisting speeds up the decay of the heat kernel with respect to the case of straight untwisted tubes moreover the above large time decay is valid for a wide class of subcritical operators defined on a straight tube we also discuss some applications of this result such as sobolev inequalities and spectral estimates for schrodinger operators delta d omega v

criticality theory for schrodinger operators with singular potential abstract this paper extends a weighted spectral gap classification for schrodinger operators v to a large class of locally integrable potentials v called balanced potentials here harnack s inequality will not hold in general for such potentials in addition to the standard potentials in the space l l o c p for some p n 2 this class contains potentials for which v is locally bounded with no restriction on v or more generally those for which the positive and negative singularities are separated as well as those for which the interaction of the positive and negative singularities is not too strong we also establish for such potentials under the additional assumption that v l l o c p for some p n 2 versions of the agmon allegretto piepenbrink principle characterising the subcritical critical operators in terms of the cone of positive distributional super solutions

galerkin approximation of optimal linear filtering of infinite dimensional linear systems in this paper an implementable approximation of the infinite dimensional kalman filter is proposed for linear distributed systems corrupted by white noise it relies on a galerkin type treatment of both the riccati and the filter equations and it is shown to converge to the best linear estimate of the state for each sample path of the noise a basic tool is the study of the riccati equation on the hilbert space of hilbert schmidt operators on the state space numerical results are given for a case concerning delay differential equation

density estimation in the presence of heteroscedastic measurement error of unknown type using phase function deconvolution it is important to properly correct for measurement error when estimating density functions associated with biomedical variables these estimators that adjust for measurement error are broadly referred to as density deconvolution estimators while most methods in the literature assume the distribution of the measurement error to be fully known a recently proposed method based on the empirical phase function epf can deal with the situation when the measurement error distribution is unknown the epf density estimator has only been considered in the context of additive and homoscedastic measurement error however the measurement error of many biomedical variables is heteroscedastic in nature in this paper we developed a phase function approach for density deconvolution when the measurement error has unknown distribution and is heteroscedastic a weighted epf wepf is proposed where the weights are used to adjust for heteroscedasticity of measurement error the asymptotic properties of the wepf estimator are evaluated simulation results show that the weighting can result in large decreases in mean integrated squared error when estimating the phase function the estimation of the weights from replicate observations is also discussed finally the construction of a deconvolution density estimator using the wepf is compared with an existing deconvolution estimator that adjusts for heteroscedasticity but assumes the measurement error distribution to be fully known the wepf estimator proves to be competitive especially when considering that it relies on minimal assumption of the distribution of measurement error

on positivity criticality and the spectral radius of the shuttle operator for elliptic operators in this paper we study the shuttle operator for a second order linear elliptic operator p on a noncompact manifold x zhao has introduced and studied the shuttle operator and its relation to the theory of positive solutions in the case of small perturbations of the laplacian in ir n 3 zhao was motivated by works of chung and varadhan which consider one dimensional schrodinger operators the main purpose of the paper is to extend the above studies we prove that in the general case the spectral radius of the shuttle operator is strictly less equal or strictly greater than 1 if and only if the operator p is respectively subcritical critical or supercritical in x we demonstrate the usefulness of the characterization for proving theorems our approach is purely analytic this research was partially supported by the israel science foundation administered by the israel academy of sciences and humanities and by the fund for the promotion of research at the technion

radial solutions of a semilinear elliptic problem we analyse the set of nonnegative global and radial solutions radial solutions for short of the equation u u p f in r n n 1 where 0 where graphics when f r c r2p 1 p h r with h r o r2p 1 p as r radial solutions continue to exist if h r is sufficiently small at infinity existence however breaks down if h r 0 graphics whenever they exist radial solutions are characterised in terms of their asymptotic behaviour as r

on families of optimal hardy weights for linear second order elliptic operators abstract we construct families of optimal hardy weights for a subcritical linear second order elliptic operator using a one dimensional reduction more precisely we first characterize all optimal hardy weights with respect to one dimensional subcritical sturm liouville operators on a b a b and then apply this result to obtain families of optimal hardy inequalities for general linear second order elliptic operators in higher dimensions as an application we prove a new rellich inequality

quantum scattering at low energies for a class of negative slowly decaying potentials including v x x with 0 2 we study the quantum mechanical scattering theory in the low energy regime using appropriate modifiers of the isozaki kitada type we show that scattering theory is well behaved on the whole continuous spectrum of the hamiltonian including the energy 0 we show that the modified scattering matrices s are welldefined and strongly continuous down to the zero energy threshold similarly we prove that the modified wave matrices and generalized eigenfunctions are norm continuous down to the zero energy if we use appropriate weighted spaces these results are used to derive oscillatory asymptotics of the standard short range and dollard type s matrices for the subclasses of potentials where both kinds of s matrices are defined for potentials whose leading part is x we show that the location of singularities of the kernel of s experiences an abrupt change from passing from positive energies to the limiting energy 0 this change corresponds to the behaviour of the classical orbits under stronger conditions one can extract the leading term of the asymptotics of the kernel of s at its singularities

a probabilistic approach to bounded positive solutions for schrodinger operators with certain classes of potentials consider the equation 1 2 u vu 0 in r d for d 3 for certain classes of potentials v we use probabilistic tools to study the bounded solutions and the positive solutions for a primary motivation is to offer probabilistic intuition for the results

dirichlet parabolicity and l1 liouville property under localized geometric conditions abstract we shed a new light on the l 1 liouville property for positive superharmonic functions by providing many evidences that its validity relies on geometric conditions localized on large enough portions of the space we also present examples in any dimension showing that the l 1 liouville property is strictly weaker than the stochastic completeness of the manifold the main tool in our investigations is represented by the potential theory of a manifold with boundary subject to dirichlet boundary conditions the paper incorporates under a unifying viewpoint some old and new aspects of the theory with a special emphasis on global maximum principles and on the role of the dirichlet green s kernel

large time behavior of the lp norm of schrodinger semigroups abstract letv 0 v c0 rv with v 3 be such that h 1 2 v 0 but for any e 0 1 2 1 e v is not positive we determine the exact rate of divergence of the norm of e th as a map from l to l a number of related problems are discussed

on positive solutions of second order elliptic equations stability results and classification soit p un operateur uniformement elliptique d ordre 2 defini dans un domaine cr n soit p le cone convexe de toutes les solutions positives de l equation pu 0 dans on etudie les proprietes generales de p pour p et generaux

criticality and ground states for second order elliptic equations abstract let p be a second order elliptic operator in a domain r n suppose that p admits a positive minimal green function g p in it is the main purpose of this paper to prove that if w c is a small perturbation of p in then max w x 0 min w x 0 t u u g p outside a compact set in

generalized transition fronts for one dimensional almost periodic fisher kpp equations this paper investigates the existence of generalized transition fronts for fisher kpp equations in one dimensional almost periodic media assuming that the linearized elliptic operator near the unstable steady state admits an almost periodic eigenfunction we show that such fronts exist if and only if their average speed is above an explicit threshold this hypothesis is satisfied in particular when the reaction term does not depend on x or in some cases is small enough moreover except for the threshold case the fronts we construct and their speeds are almost periodic in a sense when our hypothesis is no longer satisfied such generalized transition fronts still exist for an interval of average speeds with explicit bounds our proof relies on the construction of sub and super solutions based on an accurate analysis of the properties of the generalized principal eigenvalues

a new approach to pointwise heat kernel upper bounds on doubling metric measure spaces abstract on doubling metric measure spaces endowed with a strongly local regular dirichlet form we show some characterisations of pointwise upper bounds of the heat kernel in terms of global scale invariant inequalities that correspond respectively to the nash inequality and to a gagliardo nirenberg type inequality when the volume growth is polynomial this yields a new proof and a generalisation of the well known equivalence between classical heat kernel upper bounds and relative faber krahn inequalities or localised sobolev or nash inequalities we are able to treat more general pointwise estimates where the heat kernel rate of decay is not necessarily governed by the volume growth a crucial role is played by the finite propagation speed property for the associated wave equation and our main result holds for an abstract semigroup of operators satisfying the davies gaffney estimates

an analysis of optimal modal regulation convergence and stability this paper treats the linear quadratic regulator problem for infinite dimensional second order in time linear oscillators we solve the problem approximately by modeling a finite number of mode

brief paper on the stability of a reduced order filter based on dominant singular value decomposition of the system dynamics the stability of a reduced order filter rof the gain of which is constructed on the basis of a subspace of dominant singular vectors of the system dynamics is examined a definition of s detectability is introduced it is found that the observability of all unstable and neutral singular vectors s detectability is a sufficient condition for the existence of a stable filter

plancherel type estimates and sharp spectral multipliers abstract we study general spectral multiplier theorems for self adjoint positive definite operators on l2 x where x is any open subset of a space of homogeneous type we show that the sharp hormander type spectral multiplier theorems follow from the appropriate estimates of the l2 norm of the kernel of spectral multipliers and the gaussian bounds for the corresponding heat kernel the sharp hormander type spectral multiplier theorems are motivated and connected with sharp estimates for the critical exponent for the riesz means summability which we also study here we discuss several examples which include sharp spectral multiplier theorems for a class of scattering operators on r3 and new spectral multiplier theorems for the laguerre and hermite expansions

simulation extrapolation the measurement error jackknife abstract this article provides theoretical support for our simulation based estimation procedure simex for measurement error models we do so by establishing a strong relationship between simex estimation and jackknife estimation a result of our investigation is the identification of a variance estimation method for simex that parallels jackknife variance estimation data from the framingham heart study are used to illustrate the variance estimation procedure in logistic regression measurement error models

maximum and anti maximum principlesand eigenfunctions estimates via perturbation theory of positive solutions of elliptic equations in this paper we discuss some new results concerning perturbation theory for second order elliptic partial differential equations related to positivity properties of such equations we continue the study of some different notions of small perturbations and discuss their relations to comparisons of green s functions refined maximum and anti maximum principles ground state and the decay of eigenfunctions in particular we show that if v is a positive function which is a semismall perturbation of a subcritical schrodinger operator h defined on a domain omega subset mathbb r d and phi k k geq 0 are the dirichlet eigenfunctions of the equation hu lambda vu then for any k geq 0 the function phi k phi 0 is bounded and has a continuous extension up to the martin boundary of the pair omega h where phi 0 is the ground state of h with a principal eigenvalue lambda 0

sharp condition on the decay of the potential for the absence of a zero energy ground state of the schrodinger equation the authors prove a sharp criterion on the decay of the potential of a schrodinger operator on r3 that ensures the absence of a zero energy ground state this condition complements results due to simon and lieb 1981 they also give an improved version of their results which however is still not optimal

an efficient algorithm for estimating noise covariances in distributed systems we present an efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochasticdynamic systems such systems arise typically by discretizing distributed parameter systems and their size renders computational efficiency a major consideration our adaptive filtering algorithm is based on the ideas of belanger and is algebraically equivalent to his algorithm the earlier algorithm however has computational complexity proportional to p6 where p is the number of observations of the system state while the new algorithm has complexity proportional to only p3 furthermore our formulation of noise covariance estimation as a secondary filter analogous to state estimation as a primary filter suggests several generalizations of the earlier algorithm the performance of the proposed algorithm is demonstrated for a distributed system arising in numerical weather prediction

differentiability of spectral functions for symmetric alpha stable processes let be a signed radon measure in the kato class and define a schrodinger type operator h 1 2 2 on r d we show that its spectral bound c inf h is differentiable if d 2 and is green tight

structure of positive solutions to δ v u 0 in rn on etudie la structure de toutes les solutions positives d une equation de schrodinger stationnaire ou le potentiel v est suppose etre une fonction a valeur reelle appartenant a l p loc r n avec p n 2 pour n 2 et p 1 pour n 1 on considere une formule de representation explicite pour des solutions positives leurs asymptotes a l infini et le probleme de dirichlet avec une condition aux limites a l infini

the optimal reduced order estimator for systems with singular measurement noise the optimal reduced order estimator is completely characterized by necessary conditions resulting from the optimal projection equations the solution consists of one riccati equation and two lyapunov equations coupled by two projections explicit expressions for all of the estimator parameters are given the relation between the reduced order singular estimator and the full order optimal singular estimator which is of reduced order itself is investigated it is shown that under certain conditions the optimal estimator is recovered from the reduced order estimator

optimal hardy weight for second order elliptic operator an answer to a problem of agmon abstract for a general subcritical second order elliptic operator p in a domain r n or noncompact manifold we construct hardy weight w which is optimal in the following sense the operator p w is subcritical in for all 1 null critical in for 1 and supercritical near any neighborhood of infinity in for any 1 moreover if p is symmetric and w 0 then the spectrum and the essential spectrum of w 1 p are equal to 1 and the corresponding agmon metric is complete our method is based on the theory of positive solutions and applies to both symmetric and nonsymmetric operators the constructed hardy weight is given by an explicit simple formula involving two distinct positive solutions of the equation p u 0 the existence of which depends on the subcriticality of p in

integral representations of nonnegative solutions for parabolic equations and elliptic martin boundaries abstract we consider nonnegative solutions of a parabolic equation in a cylinder d 0 t where d is a noncompact domain of a riemannian manifold under the assumption iu i e the associated heat kernel is intrinsically ultracontractive we establish an integral representation theorem any nonnegative solution is represented uniquely by an integral on d 0 m d 0 t where m d is the martin boundary of d for the associated elliptic operator we apply it in a unified way to several concrete examples to explicitly represent nonnegative solutions we also show that iu implies the condition sp i e the constant function 1 is a small perturbation of the elliptic operator on d

acceleration of stochastic approximation by averaging a new recursive algorithm of stochastic approximation type with the averaging of trajectories is investigated convergence with probability one is proved for a variety of classical optimization and identification problems it is also demonstrated for these problems that the proposed algorithm achieves the highest possible rate of convergence

likelihood analysis for errors in variables regression with replicate measurements summary this paper advocates likelihood analysis for regression models with measurement errors in explanatory variables for data problems in which the relevant distributions can be adequately modelled although computationally difficult maximum likelihood estimates are more efficient than those based on first and second moment assumptions and likelihood ratio inferences can be substantially better than those based on asymptotic normality of estimates the em algorithm is presented as a straightforward approach for likelihood analysis of normal linear regression with normal explanatory variables and normal replicate measurements likelihood methods for regression analysis with explanatory variable measurement error have received little attention relative to methods based on first and second moment assumptions largely because of computational difficulties uncertainty about the robustness of likelihood methods and the belief that the simpler methods perform just as well in practice with improved computational tools for likelihood analysis as discussed for example by tanner 1993 it is worthwhile to reinvestigate these issues in particular the common belief that the simpler methods perform just as well as likelihood methods may be naive first the comparison is usually cast in terms of efficiency without regard to test and confidence interval validity likelihood ratio tests and confidence intervals can be substantially better than tests and confidence intervals based on estimates and standard errors of the commonly used method of moments approaches the sampling distributions of the estimators are very often skewed especially if the measurement errors are large furthermore knowledge about the relative efficiency of the moment methods comes from a small number of efficiency comparisons from simulations of isolated situations in papers promoting these simpler methods carroll rupert stefanski 1995 7 1 an important and often overlooked issue is that the moment methods may be especially inappropriate when the distribution of the true covariates is skewed pierce et al 1992 section 2 discusses computational approaches and difficulties associated with likelihood analysis in the measurement error problem generally section 3 illustrates the em algorithm dempster laird rubin 1977 for likelihood analysis of normal linear regression with a normally distributed explanatory variable measured with normally distributed error when there are replicate measurements for at least some of the cases sections 5 and 6

minimum distance estimation of the errors in variables model using linear cumulant equations abstract we consider a multiple mismeasured regressor errors in variables model we develop closed form minimum distance estimators from any number of estimating equations which are linear in the third and higher cumulants of the observable variables using the cumulant estimators alters qualitative inference relative to ordinary least squares in two applications related to investment and leverage regressions the estimators perform well in monte carlos calibrated to resemble the data from our applications although the cumulant estimators are asymptotically equivalent to the moment estimators from erickson and whited 2002 the finite sample performance of the cumulant estimators exceeds that of the moment estimators

on uniqueness and nonuniqueness of the positive cauchy problem for parabolic equations with unbounded coefficients where i xi a nonnegative solution u x t of the equation lu 0 in xt x 0 t with a nonnegative initial data u x 0 u0 x is called a solution of the positive cauchy problem such a solution can be thought of as the temperature field at the time t in an n dimensional body which occupies the domain x the coefficients aij x are the components of the matrix of the thermal conductivities while the function 1 x is the heat capacity of a unit hypervolume hence nonnegative solutions of the cauchy problem are natural objects to study in particular it is of interest to know whether the

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

on critical and subcritical sturm liouville operators we study critical and subcritical sturm liouville operators k 1 ddx p ddx v in l2 a b k dx a b r defined as friedrichs extensions under most general conditions on k p and v in particular we prove the equivalence of the notions of criticality as introduced by simon and murata for an important class of potentials v

asymptotics of green functions and martin boundaries for elliptic operators with periodic coefficients abstract we give the asymptotics at infinity of a green function for an elliptic equation with periodic coefficients on r d basic ingredients in establishing the asymptotics are an integral representation of the green function and the saddle point method we also completely determine the martin compactification of r d with respect to an elliptic equation with periodic coefficients by using the exact asymptotics at infinity of the green function