相关论文: A pseudodifferential Hormander's inequality
A generalization of differential operators are pseudodifferential operators which are used for reasoning about partial differential equations with variable coefficients. A lot of useful properties about classical pseudodifferential…
We study the Mercer inequality and its operator extension for superquadratic functions. In particular, we give a more general form of the Mercer inequality by replacing some constants by positive operators. As some consequences, our results…
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…
In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups. The result is applied to give criteria for the ellipticity and the global hypoellipticity of…
This article improves the triangle inequality for complex numbers, using the Hermite-Hadamard inequality for convex functions. Then, applications of the obtained refinement are presented to include some operator inequalities. The operator…
The purpose of this note is to show how some results from the theory of partial differential equations apply to the study of pseudo-spectra of non-self-adjoint operators, which is a topic of current interest in applied mathematics.
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
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 extend the Moser-Trudinger inequality of one function to systems of orthogonal functions. Our results are asymptotically sharp when applied to the collective behavior of eigenfunctions of Schr\"odinger operators on bounded domains.
In this paper we discuss some spectral invariance results for non-smooth pseudodifferential operators with coefficients in H\"older spaces. In analogy to the proof in the smooth case of Beals and Ueberberg, we use the characterization of…
The purpose of this paper is to establish the theory of stochastic pseudo-differential operators and give its applications in stochastic partial differential equations. First, we introduce some concepts on stochastic pseudo-differential…
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…
An attempt is given to formulate the extensions of the KP hierarchy by introducing fractional order pseudo-differential operators. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the…
We consider several differential operators on compact almost-complex, almost-Hermitian and almost-K\"ahler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces…
The q-difference analog of the classical ladder operators is derived for those orthogonal polynomials arising from a class of indeterminate moments problem.
The aim of these notes is to describe some recent results concerning dispersive estimates for principally normal pseudodifferential operators. The main motivation for this comes from unique continuation problems. Such estimates can be used…
Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…
We define, in a consistent way, non-local pseudo-differential operators acting on a space of analytic functionals. These operators include the fractional derivative case. In this context we show how to solve homogeneous and inhomogeneous…
We consider a class of second-order partial differential operators $\mathscr A$ of H\"ormander type, which contain as a prototypical example a well-studied operator introduced by Kolmogorov in the '30s. We analyze some properties of the…
We establish a general, weighted Kohn-H\"ormander-Morrey formula twisted by a pseudodifferential operator. As an application, we exhibit a new class of domains for which the $\bar\partial$-Neumann problem is locally hypoelliptic.