Orthogonal Systems and Convolution Operators

R Ellis

ISBN 10: 3764369299 / ISBN 13: 9783764369293

Published by Basel Birkhäuser Basel Springer, 2003

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 238 pp. Englisch.

Seller Inventory # 9783764369293

Bibliographic Details

• Title: Orthogonal Systems and Convolution Operators
• Publisher: Basel Birkhäuser Basel Springer
• Publication Date: 2003
• Language: English
• ISBN 10: 3764369299
• ISBN 13: 9783764369293
• Binding: Buch
• Condition: Neu
• Dimensions: 235W x 188H x 35D millimeters 235 millimeters width by 188 millimeters height by 35 millimeters depth
• Weight: 606 grams

About this title

Synopsis

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.