On the notion of the finite part of divergent integrals in integral equations
type: Item
instance of: scholarly article
title: On the notion of the finite part of divergent integrals in integral equations
zbMATH Open document ID: 1040.65109
DOI: 10.1023/A:1021700706820
author: Ivan K. Lifanov
author: G. Vainikko
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: The paper suggests a unified approach to divergent integrals, by introducing the finite part of a divergent integral on the basis of the Taylor expansion and integration by parts. This covers all approaches considered earlier, viz. Cauchy principal value, singular integrals with finite part in the sense of Hadamard, and one-dimensional hypersingular integrals. The paper is highly theoretical, but the results obtained apply to the solution of equations containing singular integrals of the above type.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E05
zbMATH DE Number: 1916177
zbMATH Keywords: divergent integrals
zbMATH Keywords: singular integrals
zbMATH Keywords: hypersingular integrals
zbMATH Keywords: Cauchy principal value integral
zbMATH Keywords: Hadamard finite part integral
zbMATH Keywords: singular integral equations
reviewed by: Søren Christiansen
MaRDI profile type: Publication
full work available at URL: a:1021700706820
OpenAlex ID: W174227930
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description: scientific article; zbMATH DE number 1916177