Abel integral equations : analysis and applications /

Abel integral equations : analysis and applications /

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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 model...

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Bibliographic Details
Main Author: Gorenflo, Rudolf
Other Authors: Vessella, Sergio
Format: Book
Language:English
Published: Berlin ; New York : Springer-Verlag, [1991], ©1991
Berlin ; New York : c1990
Berlin ; New York : c1991
Berlin ; New York : c1991
Series:Lecture notes in mathematics (Springer-Verlag) ; 1461
Lecture notes in mathematics (Springer-Verlag) 1461
Subjects:
Abel integral equations
Global analysis (Mathematics)
Mathematics
Numerical analysis
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490 1 |a Lecture notes in mathematics ;  |v 1461 
500 |a This WorldCat-derived record is shareable under Open Data Commons ODC-BY, with attribution to OCLC  |5 CTY 
504 |a Includes bibliographical references (p. ) and index 
504 |a Includes bibliographical references (p. ) and index 
504 |a Includes bibliographical references (p. [195]-209) and index 
504 |a Includes bibliographical references and index 
504 |a Includes bibliographical references 
520 |a 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 
530 |a Also available in an electronic version 
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