Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems

This volume contains 16 original research papers written by participants of the 3rd Workshop on Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems, which was held at the Technische Universität Berlin, Germany, December 12-14, 2003. They deal with spectral and perturbation theory of linear operators in indefinite inner product spaces and their applications. The topics include extension theory of symmetric operators, normal operators, realization theory and models of generalized Nevanlinna functions, interpolation problems, reproducing kernel spaces, matrix and operator pencils, locally definitizable functions, and semigroups.

Résumé
This volume contains a collection of recent original research papers in operator theory in Krein spaces, on generalized Nevanlinna functions, which are closely connected with this theory, and on nonlinear eigenvalue problems. Key topics: - spectral theory for normal operators in Krein spaces - perturbation theory for selfadjoint operators in Krein spaces - models for generalized Nevanlinna functions

Contenu
Partial Non-stationary Perturbation Determinants for a Class of J-symmetric Operators.- Reproducing Kernel Spaces of Series of Fueter Polynomials.- Extremal Extensions of a C(?)-suboperator and Their Representations.- A Variational Principle for Linear Pencils of Forms.- Selfadjoint Extensions with Several Gaps: Finite Deficiency Indices.- The Spectrum of the Multiplication Operator Associated with a Family of Operators in a Banach Space.- A Factorization Model for the Generalized Friedrichs Extension in a Pontryagin Space.- Generalized Schur Functions and Augmented Schur Parameters.- On Nonmonic Quadratic Matrix Polynomials with Nonnegative Coefficients.- On Operator Representations of Locally Definitizable Functions.- Symmetric Relations of Finite Negativity.- An Operator-theoretic Approach to a Multiple Point Nevanlinna-Pick Problem for Generalized Carathéodory Functions.- Bounded Normal Operators in Pontryagin Spaces.- Scalar Generalized Nevanlinna Functions: Realizations with Block Operator Matrices.- Polar Decompositions of Normal Operators in Indefinite Inner Product Spaces.- Bounds for Contractive Semigroups and Second-Order Systems.