Operator Theory and Related Topics

1. Front Matter

   Pages i-xxiv

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2. M.G. Krein’s Contributions to Prediction Theory

   • Harry Dym

   Pages 1-15

3. M.G. Krein’s Contribution to the Moment Problem

   • Adolf A. Nudelman

   Pages 17-32

4. Solution of the Truncated Matrix Hamburger Moment Problem According to M.G. Krein

   • V. M. Adamyan, I. M. Tkachenko

   Pages 33-51

5. Extreme Points of a Positive Operator Ball

   • T. Ando

   Pages 53-66

6. M-Accretive Extensions of Sectorial Operators and Krein Spaces

   • Y. M. Arlinskii

   Pages 67-82

7. A Proof of the Continuous Commutant Lifting Theorem

   • Ramon Bruzual, Marisela Dominguez

   Pages 83-89

8. An Outer Derivation Construction on the Algebra of Singular Integral Operators with General Coefficients in Weighted Spaces and its Applications

   • V. M. Deundyak, K. A. Georgiev

   Pages 91-103

9. Self-adjoint Operators with Inner Singularities and Pontryagin Spaces

   • Aad Dijksma, Heinz Langer, Yuri Shondin, Chris Zeinstra

   Pages 105-175

10. On the Uniform Convergence Theorem of Semigroups

    • Ya. I. Grushka

    Pages 177-179

11. On Stochastic Integral, Wick Calculus and Generalized Stochastic Equations on Distribution Spaces of Non-Gaussian Infinite-dimensional Analysis

    • N. A. Kachanovsky

    Pages 181-189

12. Bistrict Plus-operators in Krein Spaces and Dichotomous Behavior of Irreversible Dynamical Systems

    • Victor Khatskevich, Leonid Zelenko

    Pages 191-203

13. Singular Operator as a Parameter of Self-adjoint Extensions

    • Volodymyr Koshmanenko

    Pages 205-223

14. Few-body Krein’s Formula

    • Pavel Kurasov, Boris Pavlov

    Pages 225-254

15. Linearization and Compact Perturbation of Self-adjoint Analytic Operator Functions

    • H. Langer, A. Markus, V. Matsaev

    Pages 255-285

16. Operator Interpretation of Resonances Generated by Some Operator Matrices

    • R. Mennicken, A. K. Motovilov

    Pages 287-302

17. Generalized Resolvents of Isometric Linear Relations in Pontryagin Spaces, I: Foundations

    • Oleg Nitz

    Pages 303-319

18. A Termwise Differentiation in the Inductive Scales of the Locally Convex Spaces

    • I. V. Orlov

    Pages 321-333

19. Operator Relations, Dynamical Systems, and Representations of a Class of Wick Algebras

    • Vasyl Ostrovskyi, Daniil Proskurin

    Pages 335-345

20. On Representations of F _n -Algebras and Invertibility Symbols

    • Slavik Rabanovich, Yuriĭ Samoĭlenko

    Pages 347-357

The present book is the second of the two volume Proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th Anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine from 18-22 August, 1997. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This second volume is devoted to operator theory and related topics. It opens with the bibliography of M. G. Krein and a number of survey papers about his work. The main part of the book consists of original research papers presenting the state of the art in operator theory and its applications. The first volume of these proceedings, entitled Differential Operators and related Topics, concerns the other aspects of the conference. The two volumes will be of interest to a wide-range of readership in pure and applied mathematics, physics and engineering sciences. Table of Contents Preface. . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Bibliography of Mark Grigorevich Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Review papers: M. G. Krein's Contributions to Prediction Theory H. Dym M. G. Krein's Contribution to the Moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 AA Nudelman Research Papers: Solution of the Truncated Matrix Hamburger Moment Problem according to M. G. Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Y. M. Adamyan and I. M. Tkachenko Extreme Points of a Positive Operator Ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 T. Ando M-accretive Extensions of Sectorial Operators and Krein Spaces . . . . . . . . . 67 Y. M. Arlinskii A Simple Proof of the Continuous Commutant Lifting Theorem . . . . . . . . . . 83 R. Bruzual and M.

• Operator theory
• Singular integral
• calculus
• differential equation
• differential operators
• distribution

• Department of Theoretical Physics, University of Odessa, Odessa, Ukraine

  V. M. Adamyan

• Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel

  I. Gohberg

• Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

  M. Gorbachuk, V. Gorbachuk

• Department of Mathematics, Vrije Universiteit, HV Amsterdam, The Netherlands

  M. A. Kaashoek

• Department of Mathematics, Technical University of Vienna, Vienna, Austria

  H. Langer

• Institute of Mathematics, Economics and Mechanics, Odessa State University, Odessa, Ukraine

  G. Popov

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