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Title
Integral equations with difference kernels on finite intervals [electronic resource] / Lev A. Sakhnovich.
Edition
Second edition, revised and extended
ISBN
9783319164892 electronic book
3319164899 electronic book
9783319164885
Published
Cham : Birkhäuser, [2015]
Language
English
Description
1 online resource.
Item Number
10.1007/978-3-319-16489-2 doi
Call Number
QA431
Dewey Decimal Classification
515/.45
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (viewed May 14, 2015).
Series
Operator theory. advances and applications ; v. 84.
Available in Other Form
Print version: 9783319164885
Preface to the second edition
Introduction to the first edition
1.Invertible Operator with a Difference Kernel
2.Equations of the First Kind with a Difference Kernel
3.Examples and Applications
4.Eigensubspaces and Fourier Transform
5.Integral Operators with W-Difference Kernels
6.Problems of Communication Theory
7.Levy Processes: Convolution-Type Form of the Infinitesimal Generator
8.On the Probability that the Levy Process (Class II) Remains within the Given Domain
9.Triangular Factorization and Cauchy Type Levy Processes
10.Levy Processes with Summable Levy Measures, Long Time Behavior
11.Open Problems
Commentaries and Remarks
Bibliography
Glossary
Index.
