Orthogonal Polynomials on the Unit Circle: Part 1: Classical Theory; Part 2: Spectral Theory (Colloquium Publications)

Barry Simon

Published by American Mathematical Society, 2004
ISBN 10: 0821848674 / ISBN 13: 9780821848678
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2 parts. Brand new. We distribute directly for the publisher. Clean, unmarked pages. Fine binding and cover. Ships daily. Bookseller Inventory # 1401270023

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Synopsis: This two-part volume gives a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szeg 's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by $z$ (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line. The book is suitable for graduate students and researchers interested in analysis.

Review: The author has now opened new vistas with a monumental treatise that integrates old and new aspects of the subject and describes important connections with mathematical physics, especially with spectral theory of Schrödinger Operations. ... The author has made every effort to guide the reader toward a clear understanding of the material and its various interconnections. The result is an instant classic that will become a standard source for novices and veterans alike. --Mathematical Reviews

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Title: Orthogonal Polynomials on the Unit Circle: ...
Publisher: American Mathematical Society
Publication Date: 2004
Binding: Paperback
Book Condition: New

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Barry Simon
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