Harmonic analysis in the Schwartz distribution spaces and some applications to nonclassical problems of mathematical physics
type: Item
instance of: scholarly article
title: Harmonic analysis in the Schwartz distribution spaces and some applications to nonclassical problems of mathematical physics
zbMATH Open document ID: 0935.43004
DOI: 10.1007/BF02675938
published in: Siberian Mathematical Journal
publication date: 2000-04-13T00:00:00Z
review text: The author constructs a special tool of harmonic analysis in Schwartz distribution spaces which generalizes the main facts of harmonic analysis in \(L_2(\mathbb R^2)\) to the indicated spaces. By means of this apparatus, the structure of some distributions in \(Z'(\mathbb R^n)\) with nonalgebraic singularities at isolated points is described. An essential part of this article is an application of harmonic analysis in \(Z'(\mathbb R^n)\) to the solvability of some equations with constant coefficients. The necessity of this investigation stems from the fact that solutions to these equations may have nonalgebraic singularities at isolated points. The well-posedness of some nonclassical boundary value problems of mathematical physics is studied in this class.
reviewed by: Vladimir N. Grebenev
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 35A27
Mathematics Subject Classification ID: 46E99
Mathematics Subject Classification ID: 58D25
zbMATH DE Number: 1431660
zbMATH Keywords: Schwartz distribution space
zbMATH Keywords: harmonic analysis
zbMATH Keywords: nonalgebraic singularity
author: Yu. V. Zasorin
MaRDI profile type: Publication
cites work: An Inversion Theorem for Hankel Transforms
cites work: A nonclassical boundary value problem for a three-dimensional viscous transonic equation
cites work: Q5519244
description: scientific article; zbMATH DE number 1431660