Representation of the resolvent of the Perron-Stieltjes integral equations in terms of series
type: Item
instance of: scholarly article
title: Representation of the resolvent of the Perron-Stieltjes integral equations in terms of series
zbMATH Open document ID: 0961.45001
author: D. L. Fedorov
published in: Russian Mathematics
publication date: 2000-12-07T00:00:00Z
review text: The author considers an integral equation of the form \[ x(t)=\lambda\int_a^b K(t,s) dx(s)+f(t),\quad t\in [a,b],\quad \lambda\in C, \] with matrix kernel \(K(t,s)\). Under some assumptions on the kernel he gives a representation of the resolvent by means of series. The Volterra case, when \(K(t,s)=0\), \(t<s,\) is also considered.
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 45J05
zbMATH DE Number: 1541600
zbMATH Keywords: Perron-Stieltjes integral equations
zbMATH Keywords: Fredholm integral equation
zbMATH Keywords: Volterra integral equation
zbMATH Keywords: series representation
zbMATH Keywords: matrix kernel
zbMATH Keywords: resolvent
reviewed by: N. Karapetiants
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1541600