Convolution equations of the first kind on a finite interval in Sobolev spaces
type: Item
instance of: scholarly article
title: Convolution equations of the first kind on a finite interval in Sobolev spaces
zbMATH Open document ID: 0715.47016
DOI: 10.1007/BF01732316
published in: Integral Equations and Operator Theory
publication date: 1990-01-01T00:00:00Z
review text: The convolution equation of the first kind on a finite interval \[ \int^{1}_{0}k(x-\xi)\phi (\xi)d\xi =f(x),\quad x\in (0,1) \] is studied under assumption that k(x) is a matrix-valued function, f and \(\phi\) are vector-valued functions. The aim of the investigation is to obtain Fredholm properties of this equation - in the usual setting when \(\phi\) and f belong to the different Sobolev-type space connected with ``restriction'' of functions in \(L^{\mu}_ 2({\mathbb{R}}^ 1)\) onto [0,1]. The authors give some theorems on the Fredholm properties and the invertibiliy of the Wiener-Hopf operator associated with the above equation. They also study the example arising from wave diffraction by a strip.
reviewed by: S. G. Samko
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47A50
zbMATH DE Number: 4177934
zbMATH Keywords: convolution equation of the first kind
zbMATH Keywords: matrix-valued function
zbMATH Keywords: Fredholm properties
zbMATH Keywords: invertibiliy of the Wiener-Hopf operator
zbMATH Keywords: wave diffraction by a strip
author: M. Amélia Bastos
author: António F. dos Santos
MaRDI profile type: Publication
cites work: Q3331506
cites work: The Sommerfeld problem revisited: Solution spaces and the edge conditions
cites work: Convolution equations on a finite segment and factorization of elliptic matrices
full work available at URL: https://doi.org/10.1007/bf01732316
OpenAlex ID: W2053122674
description: scientific article; zbMATH DE number 4177934