On the product integration method for solving singular integral equations in scattering theory
type: Item
instance of: scholarly article
title: On the product integration method for solving singular integral equations in scattering theory
zbMATH Open document ID: 0661.65140
DOI: 10.1016/0377-0427(89)90077-0
published in: Journal of Computational and Applied Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The author considers integral equations of the form \[ K(\lambda,\mu)=A(\lambda,\mu)+\int^{\infty}_{0}\frac{A(\lambda,\eta)K( \eta,\mu)d\eta}{\mu -\eta},\quad \mu >0 \] where the integral has a Cauchy principal value. Using product integration techniques, he shows that under certain hypotheses there exists a unique solution to the equation, and constructs an approximating sequence of functions which converges to the solution. It is also shown that the integral operator involved is compact. The treatment is abstract and no examples are given.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 4080862
zbMATH Keywords: scattering theory
zbMATH Keywords: product integration method
zbMATH Keywords: compact integral operator
zbMATH Keywords: Cauchy principal value
author: B. S. Bertram
MaRDI profile type: Publication
full work available at URL: 0377-0427(89)90077-0
OpenAlex ID: W2079288708
cites work: Approximate solutions of integral and operator equations
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description: scientific article; zbMATH DE number 4080862