Orthogonal systems and convolution operators /
The main concern of this book is the distribution of zeros of polynomials that are orthogonal on the unit circle with respect to an indefinite weighted scalar or inner product. The first theorem of this type, proved by M.G. Krein, was a far-reaching generalization of G. Szegö's result for the p...
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| Format: | eBook |
| Language: | English |
| Published: |
Basel ; Boston :
Birkhäuser Verlag,
[2003]
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| Series: | Operator theory, advances and applications ;
v. 140. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | The main concern of this book is the distribution of zeros of polynomials that are orthogonal on the unit circle with respect to an indefinite weighted scalar or inner product. The first theorem of this type, proved by M.G. Krein, was a far-reaching generalization of G. Szegö's result for the positive definite case. A continuous analogue of that theorem was proved by Krein and H. Langer. These results, as well as many generalizations and extensions, are thoroughly treated in this book. A unifying theme is the general problem of orthogonalization with invertible squares in modules over C*-algebras. Particular modules that are considered in detail include modules of matrices, matrix polynomials, matrix-valued functions, linear operators, and others. One of the central features of this book is the interplay between orthogonal polynomials and their generalizations on the one hand, and operator theory, especially the theory of Toeplitz marices and operators, and Fredholm and Wiener-Hopf operators, on the other hand. The book is of interest to both engineers and specialists in analysis. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xvi, 236 pages) |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliography: | Includes bibliographical references (pages [227]-231) and indexes. |
| ISBN: | 9783034880459 (electronic bk.) 3034880456 (electronic bk.) |