Pseudodifferential operators with analytic symbols
type: Item
instance of: scholarly article
title: Pseudodifferential operators with analytic symbols
zbMATH Open document ID: 0870.35132
DOI: 10.1007/BF02683842
author: V. N. Nalimov
published in: Siberian Mathematical Journal
publication date: 1997-08-07T00:00:00Z
review text: Under study is the action of pseudodifferential operators, with symbols \(\hat k(\xi)\) analytic in the strip \(|\Im \xi|\leq\rho\), in the scale \(V^s(\rho)\) of Banach spaces of distributions on the real axis. Each element of \(V^s(\rho)\) is a sum of distributions periodic at both infinities with period \(L\) and belonging to the class \(H^s(0,L)\), which are fused together by an exponentially decreasing function of the class \(E^s(\rho)\). The basic properties of such operators are described. As an application, the author considers the boundary value problem for harmonic functions in a strip with discontinuous boundary data. Properties of eigenfunctions are described and necessary and sufficient conditions are found for the existence of a solution.
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 30E25
Mathematics Subject Classification ID: 31A25
zbMATH DE Number: 1046602
zbMATH Keywords: convolution operators
zbMATH Keywords: boundary value problem
zbMATH Keywords: conjugation problem
MaRDI profile type: Publication
cites work: Q3673307
cites work: Q5519336
cites work: Q5515593
description: scientific article; zbMATH DE number 1046602