Partial integral equations of the third kind
type: Item
instance of: scholarly article
title: Partial integral equations of the third kind
zbMATH Open document ID: 1163.45001
author: A. S. Kalitvin
published in: Journal of Mathematical Sciences (New York)
publication date: 2008-09-03T00:00:00Z
review text: The author investigates partial integral equations of the third kind, that is, \(Cx=(L+M+N)x+f\), where \(C,L,M,N\) are linear operators on the space of continuous functions defined on \([a,b]\times[c,d]\). Conditions under which such equations are Fredholm and Fredholm of index zero are given. Note that an equation \(Ax=f\) in a complex Banach space is Fredholm if \(A\) is a closed bounded linear operator whose range is closed, the dimension of the kernel \(n(A)\) and of the cokernel \(d(A)\) are finite. The index of the operator is \(ind\,A=n(A)-d(A)\).
reviewed by: Elena Resmerita
Mathematics Subject Classification ID: 45A05
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 5319797
zbMATH Keywords: linear integral equation
zbMATH Keywords: Fredholm equation (of index zero)
zbMATH Keywords: integrally bounded function
zbMATH Keywords: partial integral equations of the third kind
MaRDI profile type: Publication
full work available at URL: s10958-007-0349-1
OpenAlex ID: W2045795605
cites work: Q4704756
cites work: Q4951124
cites work: Q4490803
cites work: Q3749642
cites work: Perturbation theory for linear operators.
cites work: On partial integral equations in the space of continuous functions
DOI: 10.1007/S10958-007-0349-1
description: scientific article; zbMATH DE number 5319797