On integral equations in mean values in spaces of almost periodic functions
type: Item
instance of: scholarly article
title: On integral equations in mean values in spaces of almost periodic functions
zbMATH Open document ID: 0831.45002
author: M. F. Kulagina
published in: Russian Mathematics
publication date: 1996-01-03T00:00:00Z
review text: We study the properties of the operator \[ \widetilde K \varphi (t) = \lim_{T \to \infty} (2T)^{-1} \int^T_{-T} K(t,s) \varphi (s)ds \tag{1} \] in spaces of almost periodic functions introduced by Bohr, Stepanov, Weyl, and Besicovitch. We introduce the generalized discrete Fourier transformation in the Besicovitch space \(B^2\) of almost periodic functions and study properties of such a transformation. We solve certain integral and integro-differential equations with operators of the form (1).
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 42A75
zbMATH DE Number: 815681
zbMATH Keywords: integral equations
zbMATH Keywords: mean values
zbMATH Keywords: spaces of almost periodic functions
zbMATH Keywords: almost periodic solutions
zbMATH Keywords: generalized discrete Fourier transformation
zbMATH Keywords: Besicovitch space
zbMATH Keywords: integro-differential equations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 815681