Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Operator Theory: Advances and Applications (OT, volume 84)
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Table of contents (11 chapters)
Keywords
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 thathas 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)
Authors and Affiliations
Bibliographic Information
Book Title: Integral Equations with Difference Kernels on Finite Intervals
Book Subtitle: Second Edition, Revised and Extended
Authors: Lev A. Sakhnovich
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/978-3-319-16489-2
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-16488-5Published: 18 May 2015
Softcover ISBN: 978-3-319-30763-3Published: 18 May 2015
eBook ISBN: 978-3-319-16489-2Published: 05 May 2015
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 2
Number of Pages: XVIII, 226
Number of Illustrations: 2 b/w illustrations
Topics: Integral Equations, Operator Theory, Probability Theory and Stochastic Processes