Interpolation Theory and Its Applications

  • L. A. Sakhnovich

Part of the Mathematics and Its Applications book series (MAIA, volume 428)

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. L. A. Sakhnovich
    Pages 23-35
  3. L. A. Sakhnovich
    Pages 52-65
  4. L. A. Sakhnovich
    Pages 66-79
  5. L. A. Sakhnovich
    Pages 80-91
  6. L. A. Sakhnovich
    Pages 92-108
  7. L. A. Sakhnovich
    Pages 137-147
  8. L. A. Sakhnovich
    Pages 148-174
  9. L. A. Sakhnovich
    Pages 175-187
  10. Back Matter
    Pages 188-197

About this book

Introduction

1. Interpolation problems play an important role both in theoretical and applied investigations. This explains the great number of works dedicated to classical and new interpolation problems ([1)-[5], [8), [13)-[16], [26)-[30], [57]). In this book we use a method of operator identities for investigating interpo­ lation problems. Following the method of operator identities we formulate a general interpolation problem containing the classical interpolation problems (Nevanlinna­ Pick, Caratheodory, Schur, Humburger, Krein) as particular cases. We write down the abstract form of the Potapov inequality. By solving this inequality we give the description of the set of solutions of the general interpolation problem in the terms of the linear-fractional transformation. Then we apply the obtained general results to a number of classical and new interpolation problems. Some chapters of the book are dedicated to the application of the interpola­ tion theory results to several other problems (the extension problem, generalized stationary processes, spectral theory, nonlinear integrable equations, functions with operator arguments). 2. Now we shall proceed to a more detailed description of the book contents.

Keywords

Finite Identity difference equation equation extrema fourier analysis function mathematics measure variable

Authors and affiliations

  • L. A. Sakhnovich
    • 1
  1. 1.Ukrainian State Academy of CommunicationOdessaUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-0059-2
  • Copyright Information Springer Science+Business Media B.V. 1997
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-6516-0
  • Online ISBN 978-94-009-0059-2
  • About this book