Operator Theory in Inner Product Spaces

This volume contains contributions written by participants of the 4th Workshop on Operator Theory in Krein Spaces and Applications, which was held at the TU Berlin, Germany, December 17 to 19, 2004. The workshop covered topics from spectral, perturbation and extension theory of linear operators and relations in inner product spaces, including spectral analysis of differential operators, the theory of generalized Nevanlinna functions and related classes of functions, spectral theory of matrix polynomials, and problems from scattering theory.

Contributors: T.Ya. Azizov, J. Behrndt, V. Derkach, A. Fleige, K.-H. Förster, S. Hassi, P. Jonas, M. Kaltenbäck, I. Karabash, A. Kostenko, H. Langer, A. Luger, C. Mehl, B. Nagy, H. Neidhart, V. Pivovarchik, J. Rehberg, L. Rodman, A. Sandovici, H. de Snoo, L.I. Soukhotcheva, C. Trunk, H. Winkler, H. Woracek

Linear Operators in Almost Krein Spaces.- Generalized Resolvents of a Class of Symmetric Operators in Krein Spaces.- Block Operator Matrices, Optical Potentials, Trace Class Perturbations and Scattering.- Asymptotic Expansions of Generalized Nevanlinna Functions and their Spectral Properties.- A Necessary Aspect of the Generalized Beals Condition for the Riesz Basis Property of Indefinite Sturm-Liouville Problems.- On Reducible Nonmonic Matrix Polynomials with General and Nonnegative Coefficients.- On Exceptional Extensions Close to the Generalized Friedrichs Extension of Symmetric Operators.- On the Spectrum of the Self-adjoint Extensions of a Nonnegative Linear Relation of Defect One in a Krein Space.- Canonical Differential Equations of Hilbert-Schmidt Type.- Spectral Analysis of Differential Operators with Indefinite Weights and a Local Point Interaction.- Normal Matrices in Degenerate Indefinite Inner Product Spaces.- Symmetric Hermite-Biehler Polynomials with Defect.- A Note on Indefinite Douglas’ Lemma.- Some Basic Properties of Polynomials in a Linear Relation in Linear Spaces.