Spectral Theory in Inner Product Spaces and Applications 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, Berlin, December 2006

This book contains a collection of recent research papers originating from the 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, which was held at the TU Berlin, Germany, December 14 to 17, 2006. The contributions in this volume are devoted to spectral and perturbation theory of linear operators in spaces with an inner product, generalized Nevanlinna functions and problems and applications in the field of differential equations. Among the discussed topics are linear relations, singular perturbations, de Branges spaces, nonnegative matrices and abstract kinetic equations. TOC:Preface.- Research Articles.

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.