Related papers: Non-Local Pseudo-Differential Operators
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…
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…
In this paper we use different techniques from the fractional and pseudo-operators calculus to solve partial differential equations involving operators with non integer exponents. We apply the method to equations resembling generalizations…
The importance of the theory of pseudo-differential operators in the study of non linear integrable systems is point out. Principally, the algebra $\Xi $ of nonlinear (local and nonlocal) differential operators, acting on the ring of…
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…
This paper deals with the multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoelliptic operators, with homogeneous multi-point time-nonlocal…
We define a family of pseudodifferential operators on the Hilbert space $L^2(\mathbf{Q}_p)$ of complex valued square-integrable functions on the $p$-adic number field $\mathbf{Q}_p$. The Riemann zeta-function and the related Dirichlet…
We study the notion of non-commumative higher dimensional local fields. A simplest example is the ring P of formal pseudo- differential operators. As an application we extend the KP hierarchy to the space $P^n$.
We consider pseudodifferential operators on functions on $\R^{n+1}$ which commute with the Euler operator, and can thus be restricted to spaces of functions homogeneous of some given degree. Their symbols can be regarded as functions on a…
A systematic exposition is given of the theory of invariant differential operators on a not necessarily reductive homogeneous space. This exposition is modelled on Helgason's treatment of the general reductive case and the special…
In this work we study some general classes of pseudodifferential operators whose symbols are defined in terms of phase space estimates.
The study of nonlocal operators of fractional type possesses a long tradition, motivated both by mathematical curiosity and by real world applications...
We discuss some basic properties of the eigenfunctions of a class of nonlocal operators whose model is the fractional p-Laplacian.
In this paper, we study invariants of linear differential operators with respect to algebraic Lie pseudogroups. Then we use these invariants and the principle of n-invariants to get normal forms (or models) of the differential operators and…
Pseudodifferential operators of several variables are formal Laurent series in the formal inverses of $\partial_1, ..., \partial_n$ with $\partial_i = d$ $1 \leq i \leq n$. As in the single variable case, Lax equations can be constructed…
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.
In this article we study a class of non-Archimedean pseudodifferential operators whose symbols are negative definite functions. We prove that these operators extend to generators of Feller semigroups. In order to study these operators, we…
We develop the notions of multiplicative Lie conformal and Poisson vertex algebras, local and non-local, and their connections to the theory of integrable differential-difference Hamiltonian equations. We establish relations of these…
We provide sufficient conditions of local solvability for partial differential operators with variable Colombeau coefficients. We mainly concentrate on operators which admit a right generalized pseudodifferential parametrix and on operators…
A class of pseudodifferential operators on the Heisenberg group is defined. As it should be, this class is an algebra containing the class of differential operators. Furthermore, those pseudodifferential operators act continuously on…