Abel Integral Equations

Released on by Rudolf Gorenflo
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  • Abel Integral Equations Book Detail

  • Author : Rudolf Gorenflo
  • Release Date : 2006-11-14
  • Publisher : Springer
  • Genre : Mathematics
  • Pages : 225
  • ISBN 13 : 3540469494
  • File Size : 53,53 MB
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Abel Integral Equations by Rudolf Gorenflo PDF Summary

Book Description: 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.

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Abel Integral Equations

Abel Integral Equations

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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

Singular Integral Equations

Singular Integral Equations

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Many physical problems that are usually solved by differential equation techniques can be solved more effectively by integral equation methods. This work focuse