Operator Theory: Advances and Applications

Integral Equations with Difference Kernels on Finite Intervals

Second Edition, Revised and Extended

Authors: Sakhnovich, Lev

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  • Provides a new and effective method for solving integral equations with difference kernels
  • Uses the results obtained to investigate a number of theoretical and applied problems
  • Presents solutions to some well-known problems, in particular the M. Kac problems and a new form of the Levy-Ito equality
  • Studies a number of essential examples
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  • ISBN 978-3-319-16489-2
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About this book

This book focuses on solving integral equations with difference kernels on finite intervals. The corresponding problem on the semiaxis was previously solved by N. Wiener–E. Hopf and by M.G. Krein. The problem on finite intervals, though significantly more difficult, may be solved using our method of operator identities. This method is also actively employed in inverse spectral problems, operator factorization and nonlinear integral equations. Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M. Kac problems on stable processes. In this second edition these results are extensively generalized and include the case of all Levy processes. We present the convolution expression for the well-known Ito formula of the generator operator, a convolution expression that has proven to be fruitful. Furthermore we have added a new chapter on triangular representation, which is closely connected with previous results and includes a new important class of operators with non-trivial invariant subspaces. Numerous formulations and proofs have now been improved, and the bibliography has been updated to reflect more recent additions to the body of literature.

Reviews

“This monograph consists of 11 chapters, it is dedicated to the analysis of integral equations … . The monograph can be useful for researchers, undergraduate and graduate students in applied mathematics, whose research area is related to application of integral equations.” (Alexander N. Tynda, zbMATH 1334.45001, 2016)


Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-3-319-16489-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
Softcover $109.00
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Integral Equations with Difference Kernels on Finite Intervals
Book Subtitle
Second Edition, Revised and Extended
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
84
Copyright
2015
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-16489-2
DOI
10.1007/978-3-319-16489-2
Hardcover ISBN
978-3-319-16488-5
Softcover ISBN
978-3-319-30763-3
Series ISSN
0255-0156
Edition Number
2
Number of Pages
XVIII, 226
Number of Illustrations
2 b/w illustrations
Topics