On the theory of generalized Abel integral equations on the half-line
type: Item
instance of: scholarly article
title: On the theory of generalized Abel integral equations on the half-line
zbMATH Open document ID: 0629.45004
DOI: 10.1007/BF01201154
author: Frank Penzel
published in: Integral Equations and Operator Theory
publication date: 1987-01-01T00:00:00Z
review text: Die Arbeit basiert auf der Dissertation des Autors. Es wird der Operator untersucht, der von Systemen verallgemeinerter Abelscher Integralgleichungen \[ (*)\quad a(x)\int^{x}_{c}f(t)/(x-t)^{1- \alpha}dt+b(x)\int^{d}_{x}f(t)/(t-x)^{1-\alpha}dt=g(x) \] auf gewichtetem \(L_ p\)-Raum induziert wird. In der Einleitung werden folgende Ziele der Arbeit genannt: Für die in (*) auftretenden Funktionen sollen Bedingungen angegeben werden, unter denen der Bildbereich des Operators gut beschreibbar ist, (*) sich auf eine Fredholm-Riesz-Gleichung zurückführen läßt und (*) explizit lösbar ist. Zum Auffinden dieser Bedingungen, die überdies zu komplex sind, um kurz aufgelistet werden zu können, sind detaillierte Untersuchungen notwendig; die Beweise sind - mit Verweis auf die Dissertation - vielfach recht kurz gehalten.
Mathematics Subject Classification ID: 45F15
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 4023983
zbMATH Keywords: Abel integral equation
zbMATH Keywords: Cauchy-type integral equation
zbMATH Keywords: systems
zbMATH Keywords: range of operator
zbMATH Keywords: Fredholm-Riesz integral equation
zbMATH Keywords: explicit solvability
reviewed by: Marianne Reichert
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4023983