Overview
- Authors:
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Rudolf Gorenflo
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Sergio Vessella
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Table of contents (10 chapters)
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- Rudolf Gorenflo, Sergio Vessella
Pages 1-7
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- Rudolf Gorenflo, Sergio Vessella
Pages 8-25
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- Rudolf Gorenflo, Sergio Vessella
Pages 26-34
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- Rudolf Gorenflo, Sergio Vessella
Pages 35-63
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- Rudolf Gorenflo, Sergio Vessella
Pages 64-82
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- Rudolf Gorenflo, Sergio Vessella
Pages 83-94
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- Rudolf Gorenflo, Sergio Vessella
Pages 95-128
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- Rudolf Gorenflo, Sergio Vessella
Pages 129-153
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- Rudolf Gorenflo, Sergio Vessella
Pages 154-181
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- Rudolf Gorenflo, Sergio Vessella
Pages 182-194
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Back Matter
Pages 195-217
About this book
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.