Constructing the Neumann series -- an example
type: Item
instance of: scholarly article
title: Constructing the Neumann series -- an example
zbMATH Open document ID: 0752.45001
author: David S. Tselnik
published in: Elemente der Mathematik
publication date: 1992-06-27T00:00:00Z
full work available at URL: https://eudml.org/doc/141520
review text: The Neumann series for the integral equation \(\theta(\xi)=\theta_ 0+\nu\int^ \ell_ 0\theta(\varepsilon)K(\xi,\varepsilon)d\varepsilon\), in which \(K(\xi,\varepsilon)=\{\xi\text{ for } \xi<\varepsilon;\;\varepsilon\text{ for } \xi>\varepsilon\}\), leads to the solution \(\theta(\xi)=\theta_ 0\times\sec\sqrt \nu\ell\cos\sqrt \nu(\ell-\xi)\), for every \(\nu\) distinct of an eigenvalue \(\nu_ j=[(2j- 1)\pi/(2\ell)]^ 2\), \(j=1,2,\ldots\).
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 26733
zbMATH Keywords: Fredholm equation
zbMATH Keywords: Neumann series
reviewed by: Constantin Corduneanu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 26733