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This volume is based on the proceedings of the Toeplitz Lectures 1999 and of the Workshop in Operator Theory held in March 1999 at Tel-Aviv University and at the Weizmann Institute of Science. The workshop was held on the occasion of the 60th birthday of Harry Dym, and the Toeplitz lecturers were Harry Dym and Jim Rovnyak. The papers in the volume reflect Harry's influence on the field of operator theory and its applications through his insights, his writings, and his personality. The volume begins with an autobiographical sketch, followed by the list ofpublications ofHarry Dym and the paper ofIsrael Gohberg: On Joint Work with Harry Dym. The following paper by Jim Rovnyak: Methods of Krdn Space Operator The- ory, is based on his Toeplitz lectures. It gives a survey ofold and recents methods of KreIn space operator theory along with examples from function theory, espe- cially substitution operators on indefinite Dirichlet spaces and their relation to coefficient problems for univalent functions, an idea pioneered by 1. de Branges and underlying his proof of the Bieberbach conjecture (see [9]).
The remaining papers (arranged in the alphabetical order) can be divided into the following categories. Schur analysis and interpolation In Notes on Interpolation in the Generalized Schur Class. I, D. Alpay, T. Con- stantinescu, A. Dijksma, and J. Rovnyak use realization theory for operator colli- gations in Pontryagin spaces to study interpolation and factorization problems in generalized Schur classes.
Contents
Looking Back.- List of Publications of Harry Dym.- On Joint Work with Harry Dym.- Methods of Krein Space Operator Theory.- Notes on Interpolation in the Generalized Schur Class.I. Applications of Realization Theory.- Stable Dissipative Linear Stationary Dynamical Scattering Systems.- Concrete Interpolation of Meromorphic Matrix Functions on Riemann Surfaces.- On Realizations of Rational Matrix Functions of Several Complex Variables.- The Poincaré—Hardy Inequality on the Complement of a Cantor Set.- Finite Section Method for Linear Ordinary Differential Equations on the Full Line.- On the Spectral Radius of Multi-Matrix Functions.- A Generic Schur Function is an Inner One.- Abstract Interpolation Scheme for Harmonic Functions.- Chains of Space-Time Open Systems and DNA.- A Class of Robustness Problems in Matrix Analysis.- Dual Discrete Canonical Systems and Dual Orthogonal Polynomials.- Non-Selfadjoint Sturm-Liouville Operators with Multiple Spectra.
