相关论文: Dispersive estimates for principally normal pseudo…

This paper describes a new comparison principle that can be used for the comparison of space-time estimates for dispersive equations. In particular, results are applied to the global smoothing estimates for several classes of dispersive…

In this article, we prove Carleman estimates for the generalized time-fractional advection-diffusion equations by considering the fractional derivative as perturbation for the first order time-derivative. As a direct application of the…

In the development of controllability and inverse problem results for semi-discrete systems, by using Carleman estimates, it is required to estimate of the discrete operators applied to Carleman weight functions. This work aims to establish…

The purpose of the present work is to establish decorrelation estimates at distinct energies for some random Schr\"odinger operator in dimension one. In particular, we establish the result for some random operators on the continuum with…

This paper concerns about the weak unique continuation property of solutions of a general system of differential equation/inequality with a second order strongly elliptic system as its leading part. We put not only some natural assumption…

We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of weighted estimates…

We present abstract inhomogeneous Strichartz estimates for dispersive operators, extending previous work by M. Keel and T. Tao on the one hand, and generalising results of D. Foschi, M. Vilela, M. Nakamura and T. Ozawa on the other hand. It…

Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…

We establish a strong unique continuation property for stochastic parabolic equations. Our method is based on a suitable stochastic version of Carleman estimate. As far as we know, this is the first result for strong unique continuation…

The classical Hormander's inequality for linear partial differential operators with constant coeffcients is extended to pseudodifferential operators.

The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.

We study the approximation properties of pseudo-differential operators with small time-frequency dispersion, meaning that their spreading functions are supported in a small neighborhood of the origin. It is commonly assumed that for such…

Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of…

We study the phenomena that arise when we combine the standard pseudodifferential operators with those operators that appear in the study of some sub-elliptic estimates, and on strongly pseudoconvex domains. The algebra of operators we…

This is a survey, which is a continuation of the previous survey of the author about applications of Carleman estimates to Inverse Problems, J. Inverse and Ill-Posed Problems, 21, 477-560, 2013. It is shown here that Tikhonov functionals…

In this article, we focus on the analysis of discrete versions of the Calderon problem in dimension d \geq 3. In particular, our goal is to obtain stability estimates for the discrete Calderon problems that hold uniformly with respect to…

This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in…

We will show that the same type of estimates known for the fundamental solutions for scalar parabolic equations with smooth enough coefficients hold for the first order derivatives of fundamental solution with respect to space variables of…

We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…

In this work we study some general classes of pseudodifferential operators whose symbols are defined in terms of phase space estimates.