| Introduction to the Theory of Toeplitz Operators with Infinite Index 2002 Edition Contributor(s): Dybin, Vladimir (Author), Iacob, A. (Translator), Grudsky, Sergei M. (Author) |
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ISBN: 3764367288 ISBN-13: 9783764367282 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: October 2002 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Calculus - Mathematics | Mathematical Analysis - Medical |
| Dewey: 515.724 |
| LCCN: 2002190998 |
| Series: Operator Theory, Advances and Applications |
| Physical Information: 0.75" H x 6.14" W x 9.21" (1.36 lbs) 300 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: We offer the reader of this book some specimens of "infinity" that we seized from the "mathematical jungle" and trapped within the solid cage of analysis The creation of the theory of singular integral equations in the mid 20th century is associated with the names of N.1. Muskhelishvili, F.D. Gakhov, N.P. Vekua and their numerous students and followers and is marked by the fact that it relied principally on methods of complex analysis. In the early 1960s, the development of this theory received a powerful impulse from the ideas and methods of functional analysis that were then brought into the picture. Its modern architecture is due to a constellation of brilliant mathemati- cians and the scientific collectives that they produced (S.G. Mikhlin, M.G. Krein, B.V. Khvedelidze, 1. Gohberg, LB. Simonenko, A. Devinatz, H. Widom, R.G. Dou- glas, D. Sarason, A.P. Calderon, S. Prossdorf, B. Silbermann, and others). In the ensuing period, the Fredholm theory of singular integral operators with a finite index was completed in its main aspects in wide classes of Banach and Frechet spaces. |