Operator Theory and Indefinite Inner Product Spaces

In March 2004, an international conference was held in Vienna, Austria, on the occasion of the retirement of Heinz Langer, one of the leading experts in operator theory of indefinite inner product spaces. This volume contains some of the papers presented at the meeting. These fifteen refereed articles report on recent and original results in various areas of operator theory, all of them related with the work of Heinz Langer. The topics range from abstract spectral theory in Krein spaces to more concrete applications, e.g., to boundary value problems, the study of orthogonal functions or moment problems. The book closes with a historical survey paper.

The scientific part of the book is preceeded by some biographical material and some information about the conference itself. This includes the conference program, the list of participants and an updated list of publications of Heinz Langer.

Résumé

A colloquium on operator theory was held in Vienna, Austria, in March 2004, on the occasion of the retirement of Heinz Langer, a leading expert in operator theory and indefinite inner product spaces. The book contains fifteen refereed articles reporting on recent and original results in various areas of operator theory, all of them related with the work of Heinz Langer. The topics range from abstract spectral theory in Krein spaces to more concrete applications, such as boundary value problems, the study of orthogonal functions, or moment problems. The book closes with a historical survey paper.

Contenu
Research articles.- General Solution of the Stieltjes Truncated Matrix Moment Problem.- Q-functions of Quasi-selfadjoint Contractions.- A Class of Abstract Boundary Value Problems with Locally Definitizable Functions in the Boundary Condition.- Riesz Bases of Root Vectors of Indefinite Sturm-Liouville Problems with Eigenparameter Dependent Boundary Conditions, I.- Minimal Models for -functions.- Generalized Friedrichs Extensions Associated with Interface Conditions for Sturm-Liouville Operators.- Spectral Properties of Operator Polynomials with Nonnegative Coefficients.- Szeg? Pairs of Orthogonal Rational Matrix-valued Functions on the Unit Circle.- Singularities of Generalized Strings.- Orthogonal Polynomials on the Unit Circle with Respect to a Rational Weight Function.- Bi-dimensional Moment Problems and Regular Dilations.- Isospectral Vibrating Systems, Part 2: Structure Preserving Transformations.- A Functional Description for the Commutative WJ*-algebras of the D?+-class.- On Normal Extensions of Unbounded Operators: IV. A Matrix Construction.- Directing Mappings in Krein Spaces.- Survey Article.- The Extension Problem for Positive Definite Functions. A Short Historical Survey.