Collection of recent original research papers

Augmented Schur Parameters for Generalized Nevanlinna Functions and Approximation.- On Domains of Powers of Linear Operators and Finite Rank Perturbations.- Finite-dimensional de Branges Subspaces Generated by Majorants.- Trace Formulae for Dissipative and Coupled Scattering Systems.- Approximation of N ? ? -functions I: Models and Regularization.- On the Block Numerical Range of Nonnegative Matrices.- A Quantum Dot with Impurity in the Lobachevsky Plane.- One-dimensional Perturbations, Asymptotic Expansions, and Spectral Gaps.- Abstract Kinetic Equations with Positive Collision Operators.- On the Structure of Semigroups of Operators Acting in Spaces with Indefinite Metric.- G-Self-adjoint Operators in Almost Pontryagin Spaces.- On a Kre?n Criterion.- Two-sided Weighted Shifts Are 'Almost Krein' Normal.

This volume contains papers written by participants of the 6th Workshop on - erator Theory in Krein Spaces and Operator Polynomials, which was held at the Technische Universit at Berlin, Germany, December 14 to 17, 2006. This workshop was attended by 67 participants from 14 countries. The lectures covered topics from spectral and perturbation theory of linear operators in inner product spaces and from operator polynomials. They included the theory of generalized Nevanlinna and Schur functions, di?erential operators, singular perturbations, de Branges spaces, scattering problems, block numerical ranges, nonnegative matrices and relations. All these topics are re?ected in the present volume. Besides, it contains an after dinner speech from an earlier wo- shop, which we think may be of interest for the reader, as well as a speech on the occasion of the retirement of Peter Jonas. It is a pleasure to acknowledge the substantial ?nancial support received from the Deutsche Forschungsgemeinschaft (DFG), Berlin Mathematical School (BMS), DFG-Forschungszentrum MATHEON Mathematik fur Schlussel- technologien , Institute of Mathematics of the Technische Universit at Berlin. WewouldalsoliketothankPetraGrimbergerforhergreathelpintheorganisation. Without her assistance the workshop might not have taken place.