Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems

rd This volume contains papers written by the participants of the 3 Workshop on Operator Theory in Krein spaces and Nonlinear Eigenvalue Problems, held at the Technische Universit. at Berlin, Germany, December 12 to 14, 2003. The workshop covered topics from spectral, perturbation and extension t- ory of linear operators in Krein spaces. They included generalized Nevanlinna functions and related classes of functions, boundary value problems for di?erential operators, spectral problems for matrix polynomials, and perturbation problems forsecondorderevolutionequations.Alltheseproblemsarere?ectedinthepresent volume. The workshop was attended by 46 participants from 12 countries. It is a pleasure to acknowledge the substantial ?nancial support received from the - Research Training Network HPRN-CT-2000-00116 "Analysis and Operators" by the European Community, - DFG-Forschungszentrum MATHEON "Mathematik fur .. Schlussel- .. technologien", - Institute of Mathematics of the Technische Universit. at Berlin. We would also like to thank Petra Grimberger for her great help. Last but not least, special thanks are due to Jussi Behrndt, Christian Mehl and Carsten Trunk for their excellent workin the organisationof the workshopand the preparationof this volume. Without their assistance the workshop might not have taken place. The Editors Operator Theory: Advances and Applications, Vol. 162, 1-17 c 2005 Birkh. auser Verlag Basel/Switzerland Partial Non-stationary Perturbation Determinants for a Class of J-symmetric Operators Vadim Adamyan, Peter Jonas and Heinz Langer Abstract. We consider the partial non-stationary perturbation determinant (1) itA ?itH ? (t):=det e P e ,t? R.

Table of Contents:
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.