The purpose of this book is to describe the theory of Hankel operators, one of the most important classes of operators on spaces of analytic func- tions. Hankel operators can be defined as operators having infinite Hankel matrices (i. e. , matrices with entries depending only on the sum of the co- ordinates) with respect to some orthonormal basis. Finite matrices with this property were introduced by Hankel, who found interesting algebraic properties of their determinants. One of the first results on infinite Han- kel matrices was obtained by Kronecker, who characterized Hankel matri- ces of finite rank as those whose entries are Taylor coefficients of rational functions. Since then Hankel operators (or matrices) have found numerous applications in classical problems of analysis, such as moment problems, orthogonal polynomials, etc. Hankel operators admit various useful realizations, such as operators on spaces of analytic functions, integral operators on function spaces on (0,00), operators on sequence spaces. In 1957 Nehari described the bounded Hankel operators on the sequence space £2. This description turned out to be very important and started the contemporary period of the study of Hankel operators. We begin the book with introductory Chapter 1, which defines Hankel operators and presents their basic properties. We consider different realiza- tions of Hankel operators and important connections of Hankel operators with the spaces BMa and V MO, Sz. -Nagy-Foais functional model, re- producing kernels of the Hardy class H2, moment problems, and Carleson imbedding operators.
| ISBN: | 9781441930507 |
| Publication date: | 10th October 2011 |
| Author: | Vladimir V Peller |
| Publisher: | Springer an imprint of Springer New York |
| Format: | Paperback |
| Pagination: | 784 pages |
| Series: | Springer Monographs in Mathematics |
| Genres: |
Functional analysis and transforms |
The purpose of this book is to describe the theory of Hankel operators, one of the most important classes of operators on spaces of analytic func- tions. Hankel operators can be defined as operators having infinite Hankel matrices (i. e. , matrices with entries depending only on the sum of the co- ordinates) with respect to some orthonormal basis. Finite matrices with this property were introduced by Hankel, who found interesting algebraic properties of their determinants. One of the first results on infinite Han- kel matrices was obtained by Kronecker, who characterized Hankel matri- ces of finite rank as those whose entries are Taylor coefficients of rational functions. Since then Hankel operators (or matrices) have found numerous applications in classical problems of analysis, such as moment problems, orthogonal polynomials, etc. Hankel operators admit various useful realizations, such as operators on spaces of analytic functions, integral operators on function spaces on (0,00), operators on sequence spaces. In 1957 Nehari described the bounded Hankel operators on the sequence space £2. This description turned out to be very important and started the contemporary period of the study of Hankel operators. We begin the book with introductory Chapter 1, which defines Hankel operators and presents their basic properties. We consider different realiza- tions of Hankel operators and important connections of Hankel operators with the spaces BMa and V MO, Sz. -Nagy-Foais functional model, re- producing kernels of the Hardy class H2, moment problems, and Carleson imbedding operators.
Hankel Operators and Their Applications features in the following genres: Functional analysis and transforms
Hankel Operators and Their Applications is available in Paperback, Hardback
Hankel Operators and Their Applications was written by Vladimir V Peller and published by Springer an imprint of Springer New York
Hankel Operators and Their Applications has 784 pages
Yes it is part of Springer Monographs in Mathematics series