# Abel Integral Equations

## Analysis and Applications

Part of the Lecture Notes in Mathematics book series (LNM, volume 1461)

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Part of the Lecture Notes in Mathematics book series (LNM, volume 1461)

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.

Abelsche Funktion Analysis Integral equation Integral equations Linear and nonlinear Abel integral equations Potential ill-posed problems numerical analysis numerical methods operator smoothing properties

- DOI https://doi.org/10.1007/BFb0084665
- Copyright Information Springer-Verlag Berlin Heidelberg 1991
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Springer Book Archive
- Print ISBN 978-3-540-53668-0
- Online ISBN 978-3-540-46949-0
- Series Print ISSN 0075-8434
- Series Online ISSN 1617-9692
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