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Toeplitz matrices

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This book is devoted to Toeplitz and singular integral operators with symbols that have discontinuities of the oscillating type. Criteria for the normal solvability of such operators are established and several methods for describing the kernel and image spaces of the operators are presented. The approach is based on the idea of modelling discontinuities with an "infinite index" by appropriate inner functions, especially by infinite Blaschke products. The corresponding techniques have been elaborated by the authors during the last two decades, and they are applicable to both symbols with slowly and rapidly increasing arguments. Moreover, the book reveals exciting connections between invariant subspaces of the shift operator, bases in Banach spaces, and various classes of entire and meromorphic functions. The book aims at making advanced topics accessible to a broad readership. It is addressed to graduate and postgraduate students and to mathematicians interested in functional analysis, the theory of functions of a complex variable, or mathematical physics.

Integral equations. --- Toeplitz operators.

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This book features a collection of up-to-date research papers that study various aspects of general operator algebra theory and concrete classes of operators, including a range of applications. Most of the papers included were presented at the International Workshop on Operator Algebras, Toeplitz Operators, and Related Topics, in Boca del Rio, Veracruz, Mexico, in November 2018. The conference, which was attended by more than 30 leading experts in the field, was held in celebration of Nikolai Vasilevski’s 70th birthday, and the contributions are dedicated to him.

Operator theory --- analyse (wiskunde)

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This volume is dedicated to the eminent Russian mathematician Igor Borisovich Simonenko on the occasion of his 70th birthday. It consists of a selection of 15 original contributions written by leading experts in operator theory. The topics reflect the wide range and the rich variety of areas of interests, achievements and influence of I.B. Simonenko. The book also includes his biography, the complete list of publications and a list of his Ph.D. students. Among the topics covered are functional, Toeplitz and Toeplitz plus Hankel, local and nonlocal, singular integral and convolution operators, and continuous analogs of resultant operators. The contributions analyze and solve problems of factorization, irreducibility, asymptotics of determinants, finite sections, and index problems for different types of operators. Applications concern problems in financial mathematics and hydrodynamics. The book will be of interest to a wide audience of pure and applied mathematicians.

Operator theory --- analyse (wiskunde)

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Operator theory --- analyse (wiskunde)