Orthogonal Polynomials On The Unit Circle: Spectoral Theory (COLLOQUIUM PUBLICATIONS (AMER MATHEMATICAL SOC)) - Hardcover

Simon, Barry

Hardcover

ISBN 10: 0821836757 ISBN 13: 9780821836750

Publisher: Amer Mathematical Society, 2004

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 Schrodinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szego'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.

Edition details

• Publisher: Amer Mathematical Society
• Publication date: 2004
• Language: English
• ISBN 10: 0821836757
• ISBN 13: 9780821836750
• Binding: Hardcover
• Number of pages: 578