Operator Theory and Indefinite Inner Product Spaces

Introduction

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

Laudation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

Speech of Heinz Langer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Conference Programme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx

List of Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiv

Bibliography of Heinz Langer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxx

Research articles

V.M. Adamyan and I.M. Tkachenko

General Solution of the Stieltjes Truncated

Matrix Moment Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Yu.M. Arlinski˘ı, S. Hassi and H.S.V. de Snoo

Q-functions of Quasi-selfadjoint Contractions . . . . . . . . . . . . . . . . . . . . . . . . 23

J. Behrndt

A Class of Abstract Boundary Value Problems with

Locally Definitizable Functions in the Boundary Condition . . . . . . . . . . . 55

P. Binding and B. ´ Curgus

Riesz Bases of Root Vectors of Indefinite Sturm-Liouville Problems

with Eigenparameter Dependent Boundary Conditions, I . . . . . . . . . . . . . 75

A. Dijksma, A. Luger and Y. Shondin

Minimal Models for N∞κ -functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

A. Fleige, S. Hassi, H.S.V. de Snoo and H. Winkler

Generalized Friedrichs Extensions Associated with

Interface Conditions for Sturm-Liouville Operators . . . . . . . . . . . . . . . . . . . 135

K.-H. F¨orster and B. Nagy

Spectral Properties of Operator Polynomials

with Nonnegative Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

B. Fritzsche, B. Kirstein and A. Lasarow

Szeg˝o Pairs of Orthogonal Rational Matrix-valued Functions

on the Unit Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

M. Kaltenb¨ack, H. Winkler and H. Woracek

Singularities of Generalized Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

viii Table of Contents

L.V. Mikaelyan

Orthogonal Polynomials on the Unit Circle

with Respect to a Rational Weight Function . . . . . . . . . . . . . . . . . . . . . . . . . 249

D. Popovici

Bi-dimensional Moment Problems and Regular Dilations . . . . . . . . . . . . . 257

U. Prells and P. Lancaster

Isospectral Vibrating Systems, Part 2:

Structure Preserving Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

V. Strauss

A Functional Description for the Commutative WJ∗-algebras

of the D+

κ -class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

F.H. Szafraniec

On Normal Extensions of Unbounded Operators:

IV. A Matrix Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

B. Textorius

Directing Mappings in Kre˘ın Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

Survey Article

Z. Sasv´ari

The Extension Problem for Positive Definite Functions.

A Short Historical Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365