Orthogonal Systems and Convolution Operators

Ellis, Robert; Gohberg, Israel

ISBN 10: 3764369299 / ISBN 13: 9783764369293

Verlag: Birkhäuser, 2003

Beschreibung

Bestandsnummer des Verkäufers 1647356-n

Bibliografische Details

• Titel: Orthogonal Systems and Convolution Operators
• Verlag: Birkhäuser
• Erscheinungsjahr: 2003
• Sprache: Englisch
• ISBN-10: 3764369299
• ISBN-13: 9783764369293
• Einband: Hardcover
• Zustand: New

Über diesen Titel

Inhaltsangabe

1 Orthogonal Polynomials and Krein’s Theorem.- 2 Reformulations of Krein’s Theorem.- 3 Inner Products on Modules and Orthogonalization with Invertible Squares.- 4 Orthogonal Matrix Polynomials.- 5 Special Class of Block Toeplitz Matrices.- 6 Orthogonal Operator-Valued Polynomials: First Generalization.- 7 Convolution Equations on a Finite Interval.- 8 Continuous Analogues of Orthogonal Matrix Polynomials.- 9 Orthogonal Operator-Valued Polynomials.- 10 Reverse, Left and Right Orthogonalization.- 11 Discrete Infinite Analogue of Krein’s Theorem.- 12 Continuous Infinite Analogue of Krein’s Theorem.- References.- Index of Symbols.

Reseña del editor

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.