Yis ra ʿe l. Z. Gohberg Bücher

The present book is an expanded and enriched version ofthe textBasicOperator Theory, written by the first two authors more than twenty years ago. Since then the three ofus have used the basic operator theory text in various courses. This experience motivated us to update and improve the old text by including a wider variety ofbasic classes ofoperators and their applications. The present book has also been written in such a way that it can serve as an introduction to our previous booksClassesofLinearOperators, Volumes I and II. We view the three books as a unit. We gratefully acknowledge the support of the mathematical departments of Tel-Aviv University, the University of Maryland at College Park, and the Vrije Universiteit atAmsterdam. The generous support ofthe Silver Family Foundation is highly appreciated. Amsterdam, November 2002 The authors Introduction This elementary text is an introduction to functional analysis, with a strong emphasis on operator theory and its applications. It is designed for graduate and senior undergraduate students in mathematics, science, engineering, and other fields.

This book is dedicated to a theory of traces and determinants on embedded algebras of linear operators, where the trace and determinant are extended from finite rank operators by a limit process. The self-contained material should appeal to a wide group of mathematicians and engineers, and is suitable for teaching.

The annotation covers various topics related to Nevanlinna-Pick interpolation for time-varying input-output maps in both discrete and continuous cases. It begins with an introduction and preliminaries, followed by discussions on J-unitary operators, generalized point evaluation, and bounded input-output maps. The text delves into the solution of the time-varying tangential interpolation problem, providing illustrative examples and references. Additionally, the work addresses the dichotomy of systems and the invertibility of linear ordinary differential operators, exploring their properties on both the real line and half line, as well as Fredholm properties and exponentially dichotomous operators. It further examines inertia theorems for block weighted shifts, detailing one-sided and two-sided systems, asymptotic inertia, and related references. The interpolation for upper triangular operators is also discussed, including colligations, characteristic functions, explicit formulas, admissibility, and various interpolation methods such as Nevanlinna-Pick and Carathéodory-Fejér interpolation, along with mixed interpolation problems and examples. Lastly, the text addresses minimality and realization of discrete time-varying systems, focusing on observability, reachability, proofs of minimality theorems, realizations of infinite lower triangular matrices, and systems with constant state space dimension, including periodical system

The book covers a range of advanced topics in mathematical analysis and operator theory. It begins with uncertainty principles related to time-frequency operators, followed by sampling results for time-frequency transformations and uncertainty principles for Gabor and wavelet frames. The exploration of matrix-valued continuous analogues of orthogonal polynomials includes preliminary results, the study of orthogonal operator-valued polynomials, and the distribution of zeros of matrix-valued Krein functions. The discussion on band extensions delves into the real line as a limit of discrete band extensions, introducing the entropy principle and outlining key preliminaries and main results. Further, it addresses weakly positive matrix measures and generalized Toeplitz forms, highlighting their lifting properties and applications to Hankel and Hilbert transform operators. The text also tackles the reduction of the abstract four block problem to a Nehari problem, presenting main theorems and their proofs. Additionally, it examines the state space method for integro-differential equations of Wiener-Hopf type with rational matrix symbols, including an introduction, main theorems, and detailed proofs. Lastly, it discusses symbols and asymptotic expansions across various contexts, including smooth and piecewise smooth symbols on Rn and T, as well as symbols discontinuous across hyperplanes. The program of the workshop is also includ