Orthogonal Systems and Convolution Operators
By: by Robert L. Ellis, Israel Gohberg
Contributors: Gohberg, Israel
Series: Operator Theory: Advances and Applications -- 140; Operator theory, advances and applications -- 140.
Publisher: Birkhäuser Basel; Imprint: Birkhäuser
Published: 2003
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 238
ISBN-13: 9783034894180; 9783034880459
Subjects: Mathematics
Description: 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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