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Integral Equations with Difference Kernels on Finite Intervals

Second Edition, Revised and Extended

  • Lev A. Sakhnovich

Part of the Operator Theory: Advances and Applications book series (OT, volume 84)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Lev A. Sakhnovich
    Pages 1-30
  3. Lev A. Sakhnovich
    Pages 53-86
  4. Lev A. Sakhnovich
    Pages 87-99
  5. Lev A. Sakhnovich
    Pages 101-112
  6. Lev A. Sakhnovich
    Pages 113-123
  7. Lev A. Sakhnovich
    Pages 205-208
  8. Back Matter
    Pages 209-226

About this book

Introduction

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.

Keywords

Levy processes equations of the first kind generalized solutions method of operator identities triangular representation

Authors and affiliations

  • Lev A. Sakhnovich
    • 1
  1. 1.MilfordUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-16489-2
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-16488-5
  • Online ISBN 978-3-319-16489-2
  • Series Print ISSN 0255-0156
  • Series Online ISSN 2296-4878
  • Buy this book on publisher's site
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