Interpolation Theory and Its Applications

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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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.

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

• Ukrainian State Academy of Communication, Odessa, Ukraine

  L. A. Sakhnovich

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