Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations: A Volume Dedicated to Heinz Langer

Description

This volume, which is dedicated to Heinz Langer, includes biographical material and carefully selected papers. Heinz Langer has made fundamental contributions to operator theory. In particular, he has studied the domains of operator pencils and nonlinear eigenvalue problems, the theory of indefinite inner product spaces, operator theory in Pontryagin and Krein spaces, and applications to mathematical physics. His works include studies on and applications of Schur analysis in the indefinite setting, where the factorization theorems put forward by Krein and Langer for generalized Schur functions, and by Dijksma-Langer-Luger-Shondin, play a key role. The contributions in this volume reflect Heinz Langer’s chief research interests and will appeal to a broad readership whose work involves operator theory. Front Matter ....Pages i-xvi Front Matter ....Pages 1-1 List of Publications* of Professor Dr. Dr. h.c. mult. Heinz Langer (Daniel Alpay, Bernd Kirstein)....Pages 3-16 Some Pictures from the Ceremony (Daniel Alpay, Bernd Kirstein)....Pages 17-21 Heinz Langer – Pioneer of Operator Theory in Indefinite Inner Product Spaces (Bernd Kirstein)....Pages 23-69 Front Matter ....Pages 71-71 The Inverse Monodromy Problem (Damir Z. Arov, Harry Dym)....Pages 73-105 The Bitangential Matrix Nevanlinna–Pick Interpolation Problem Revisited (Joseph A. Ball, Vladimir Bolotnikov)....Pages 107-161 Finite Rank Perturbations in Pontryagin Spaces and a Sturm–Liouville Problem with λ-rational Boundary Conditions (Jussi Behrndt, Friedrich Philipp)....Pages 163-189 On Unimodular Transformations of Conservative L-systems (S. Belyi, K. A. Makarov, E. Tsekanovskiĭ)....Pages 191-215 Spectral Theory of Stationary Random Fields and their Generalizations. A Short Historical Survey (Georg Berschneider, Zoltán Sasvári)....Pages 217-235 Semicircular-like, and Semicircular Laws Induced by Certain C∗-probability Spaces over the Finite Adele Ring Aℚ (Ilwoo Cho, Palle E. T. Jorgensen)....Pages 237-280 On the Asymptotic Behaviour of the Zeros of the Solutions of a Functional-differential Equation with Rescaling (Gregory Derfel, Peter J. Grabner, Robert F. Tichy)....Pages 281-295 Rational q × q Carathéodory Functions and Central Non-negative Hermitian Measures (Bernd Fritzsche, Bernd Kirstein, Conrad Mädler)....Pages 297-320 On the Spectrum of an Operator in Truncated Fock Space (Orif O. Ibrogimov, Christiane Tretter)....Pages 321-334 Limit Properties of Eigenvalues in Spectral Gaps (Seppo Hassi, Henk de Snoo, Henrik Winkler)....Pages 335-355 Self-adjoint Boundary Conditions for the Prolate Spheroid Differential Operator (Victor Katsnelson)....Pages 357-386 An Addendum to a Paper by Li and Zhang (Lutz Klotz, Conrad Mädler)....Pages 387-392 On Accelerants and Their Analogs, and on the Characterization of the Rectangular Weyl Functions for Dirac Systems with Locally Square-Integrable Potentials on a Semi-Axis (Alexander Sakhnovich)....Pages 393-406 Dirac Equation: the Stationary and Dynamical Scattering Problems (Lev Sakhnovich)....Pages 407-424 Compressed Resolvents, Q-functions and h0-resolvents in Almost Pontryagin Spaces (Henk de Snoo, Harald Woracek)....Pages 425-484 Dissymmetrising Inner Product Spaces (Franciszek Hugon Szafraniec)....Pages 485-495