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Abel Integral Equations : Analysis and Applications / by Rudolf Gorenflo, Sergio Vessella
(Lecture Notes in Mathematics. ISSN:00758434 ; 1461)

出版者 (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年 1991
大きさ X, 222 p : online resource
書誌ID MC00023071

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eBook オンライン資料

MC000063082
SpringerLink Books Lecture Notes In Mathematics Archive 9783540469490
eBook オンライン資料

MC000063083
SpringerLink Books - AutoHoldings 9783540469490

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一般注記 Basic theory and representation formulas -- Applications of Abel's original integral equation: Determination of potentials -- Applications of a transformed abel integral equation -- Smoothing properties of the abel operators -- Existence and uniqueness theorems -- Relations between abel transform and other integral transforms -- Nonlinear abel integral equations of second kind -- Illposedness and stabilization of linear abel integral equations of first kind -- On numerical treatment of first kind abel integral equations
In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equations of the first kind problems of ill-posedness are discussed. Finally, some numerical methods are described. In the theoretical parts, emphasis is put on the aspects relevant to applications.
著者標目 *Gorenflo, Rudolf author
Vessella, Sergio author
SpringerLink (Online service)
件 名 LCSH:Mathematics
LCSH:Mathematical analysis
LCSH:Analysis (Mathematics)
LCSH:Integral equations
LCSH:Numerical analysis
LCSH:Mathematical models
LCSH:Physics
FREE:Mathematics
FREE:Integral Equations
FREE:Mathematical Modeling and Industrial Mathematics
FREE:Theoretical, Mathematical and Computational Physics
FREE:Analysis
FREE:Numerical Analysis
分 類 LCC:QA431
DC23:515.45
資料種別 機械可読データファイル
巻冊次 ISBN:9783540469490