Topics in Interpolation Theory

1. Front Matter

   Pages I-XXII

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2. Vladimir Petrovich Potapov as remembered by colleagues, friends and former students

   • Moshe Livšic

   Pages 1-18

3. On a minimum problem in function theory and the number of roots of an algebraic equation inside the unit disc

   • N. I. Akhiezer

   Pages 19-35

4. On tangential interpolation in reproducing kernel Hilbert modules and applications

   • Daniel Alpay, Vladimir Bolotnikov

   Pages 37-68

5. Notes on a Nevanlinna-Pick interpolation problem for generalized Nevanlinna functions

   • Aad Dijksma, Heinz Langer

   Pages 69-91

6. The indefinite metric in the Schur interpolation problem for analytic functions. IV

   • V. K. Dubovoj

   Pages 93-104

7. Bitangential interpolation for upper triangular operators

   • Harry Dym, Boris Freydin

   Pages 105-142

8. Bitangential interpolation for triangular operators when the Pick operator is strictly positive

   • Harry Dym, Boris Freydin

   Pages 143-164

9. Integral representations of a pair of nonnegative operators and interpolation problems in the Stieltjes class

   • Yu. M. Dyukarev

   Pages 165-184

10. On recovering a multiplicative integral from its modulus

    • Yu. P. Ginzburg

    Pages 185-193

11. On Schur functions and Szegő orthogonal polynomials

    • Leonid Golinskii

    Pages 195-203

12. Hilbert spaces of entire functions as a J theory subject

    • Leonid Golinskii, Irina Mikhailova

    Pages 205-251

13. On transformations of Potapov’s fundamental matrix inequality

    • Victor E. Katsnelson

    Pages 253-281

14. An abstract interpolation problem and the extension theory of isometric operators

    • V. E. Katsnelson, A. Ya. Kheifets, P. M. Yuditskii

    Pages 283-298

15. On the theory of matrix-valued functions belonging to the Smirnov class

    • Victor E. Katsnelson, Bernd Kirstein

    Pages 299-350

16. Integral representation of functions of class K _a

    • I. V. Kovalishina

    Pages 351-359

17. On the theory of entire matrix-functions of exponential type

    • M. G. Krein

    Pages 361-371

18. Analogs of the Nehari and Sarason theorems for character-automorphic functions and some related questions

    • Stas Kupin, Peter Yuditskii

    Pages 373-390

19. The Blaschke-Potapov factorization theorem and the theory of nonselfadjoint operators

    • M. S. Livšic

    Pages 391-396

20. Weyl matrix circles as a tool for uniqueness in the theory of multiplicative representation of J-inner matrix functions

    • Irina V. Mikhailova

    Pages 397-417

About one half of the papers in this volume are based on lectures which were pre­ sented at a conference at Leipzig University in August 1994, which was dedicated to Vladimir Petrovich Potapov. He would have been eighty years old. These have been supplemented by: (1) Historical material, based on reminiscences of former colleagues, students and associates of V.P. Potapov. (2) Translations of a number of important papers (which serve to clarify the Potapov approach to problems of interpolation and extension, as well as a number of related problems and methods) and are relatively unknown in the West. (3) Two expository papers, which have been especially written for this volume. For purposes of discussion, it is convenient to group the technical papers in this volume into six categories. We will now run through them lightly, first listing the major theme, then in parentheses the authors of the relevant papers, followed by discussion. Some supplementary references are listed at the end; OT72 which appears frequently in this volume, refers to Volume 72 in the series Operator Theory: Advances and Applications. It was dedicated to V.P. Potapov. 1. Multiplicative decompositions (Yu.P. Ginzburg; M.S. Livsic, I.V. Mikhailova; V.I. Smirnov).

• Applied Mathematics
• Finite
• Nevanlinna theory
• calculus
• complex analysis
• equation
• function
• functional analysis
• mathematics

• Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel

  H. Dym, V. Katsnelson

• Mathematisches Institut, Universität Leipzig, Leipzig, Germany

  B. Fritzsche, B. Kirstein

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