Analytic Methods of Spectral Representations of Non-Selfadjoint (Non-Unitary) Operators

by Vladimir A. Zolotarev

Overview

This book is concerned with the theory of model representations of linear non-selfadjoint and non-unitary operators. This booming area of functional analysis owes its origins to the fundamental works of M. S. Livšic on the theory of characteristic functions, the deep studies of B. S.-Nagy and C. Foias on dilation theory, and also to the Lax–Phillips scattering theory. Here, a uniform conceptual approach is developed which organically unites all these theories. New analytic methods are introduced which make it possible to solve some important problems from the theory of spectral representations. Aimed at specialists in functional analysis, the book will also be accessible to senior mathematics students.

Product Details

ISBN-13:	9783031716560
Publisher:	Springer Nature Switzerland
Publication date:	04/03/2025
Series:	Lecture Notes in Mathematics , #2355
Edition description:	Second entirely revised and enlarged Edition 2025
Pages:	540
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Vladimir A. Zolotarev graduated in 1973 from the School of Mathematics & Mechanics of V. N. Karazin Kharkiv National University, where he is now a professor. He obtained his PhD in 1978 with a thesis on multidimensional triangular models of operator systems. His doctoral thesis of 1994 was on model representations of Lie algebras of linear operators. Continuing to work at V. N. Karazin Kharkiv National University, he also joined the B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine in 2010. His main research interests are in spectral operator theory, scattering problems and inverse problems.

Table of Contents

- 1. Local Colligations and Model Representations of Linear Non-Self-Adjoint Bounded Operators.- 2. Unitary Metric Colligations and Their Model Representations.- 3. Colligations Corresponding to Unbounded Operators and Their Model Representations.- 4. Elements of V.P. Potapov's J -Theory and the Factorization Problem of J -Contractive Matrix Functions.