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Interpolation Theory and Its Applications

  • Book
  • © 1997

Overview

Authors:
  1. L. A. Sakhnovich

    1. Ukrainian State Academy of Communication, Odessa, Ukraine

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

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XVIII
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  2. Operator Identities and Interpolation Problems

    • L. A. Sakhnovich
    Pages 1-22

  3. Interpolation Problems in the Unit Circle

    • L. A. Sakhnovich
    Pages 23-35

  4. Hermitian-Positive Functions of Several Variables

    • L. A. Sakhnovich
    Pages 36-51

  5. De Branges Spaces Of Entire Functions

    • L. A. Sakhnovich
    Pages 52-65

  6. Degenerate Problems (Matrix Case)

    • L. A. Sakhnovich
    Pages 66-79

  7. Concrete Interpolation Problems

    • L. A. Sakhnovich
    Pages 80-91

  8. Extremal Problems

    • L. A. Sakhnovich
    Pages 92-108

  9. Spectral Problems For Canonical Systems Of Difference Equations

    • L. A. Sakhnovich
    Pages 109-136

  10. Integrable Nonlinear Equations (Discrete Case)

    • L. A. Sakhnovich
    Pages 137-147

  11. On Semi-Infinite Toda Chain

    • L. A. Sakhnovich
    Pages 148-174

  12. Functions with an Operator Argument

    • L. A. Sakhnovich
    Pages 175-187

  13. Back Matter

    Pages 188-197
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Keywords

About this book

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.

Authors and Affiliations

  • Ukrainian State Academy of Communication, Odessa, Ukraine

    L. A. Sakhnovich

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