Operator Theory and Related Topics

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 August 18-22, 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.

Preface

v

Table of Contents

vii

Bibliography of Mark Grigorevich Krein

ix

Review papers:

M.G. Krein's Contributions to Prediction Theory

1

(16)

H. Dym

M.G. Krein's Contribution to the Moment

17

(16)

A.A. Nudelman

Research Papers:

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

33

(34)

V.M. Adamyan

I.M. Tkachenko

Extreme Points of a Positive Operator Ball

53

T.

M-accretive Extensions of Sectorial Operators and Krein Spaces

67

(16)

Y.M. Arlinskii

A Simple Proof of the Continuous Commutant Lifting Theorem

83

(8)

R. Bruzual

M. Domingues

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

91

(14)

D. Deundyak

K. Georgiev

Self-adjoint Operators with Inner Singularities and Pontryagin Spaces

105

(72)

A. Dijksma

H. Langer

Y. Shondin

C. Zeinstra

On the Uniform Convergence Theorem for Semigroups

177

(4)

Ya. Grushka

On Stochastic Integral, Wick Calculus and Generalized Stochastic Equations on Distribution Spaces of Non-gaussian Infinite Dimensional Analysis

181

(10)

N. Kachanovsky

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

191

(14)

Khatskevich

L. Zelenko

Singular Operator as a Parameter of Self-adjoint Extensions

205

(20)

V. Koshmanenko

Few-body Krein's Formula

225

(30)

P. Kurasov

B. Pavlov

Linearization and Compact Perturbation of Self-adjoint Analytic Operator Functions

255

(32)

H. Langer

A. Markus

V. Matsaev

Operator Interpretation of Resonances Generated by Some Operator Matrices

287

(16)

R. Mennicken

A.K. Motovilov

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

303

(18)

O. Nitz

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

321

(14)

I.V. Orlov

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

335

(12)

V. Ostrovsky

D. Proskurin

On Representations of Fn-algebras and their Applications

347

(12)

S. Rabanovich

Y. Samoilenko

Ergodic Theorems with Rates for R-times Integrated Solution Families

359

(14)

Shaw Sen-Yen

Stochastic Equations in the Space of Formal Series: Convergence of Solution

373

(16)

I. Spectorsky

A Trigonometric Moment Problem for Z2

389

(16)

I. Suciu

Canonical Factorization of J -contractive-valued Functions

405

(12)

A. Tikhonov

Table of Contents of Volume I

417

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Operator Theory and Related Topics

Summary

Table of Contents

Supplemental Materials