Orthogonal polynomials on the unit circle. Part 1, Classical theory / Barry Simon.

Format:

Book

Author/Creator:

Simon, Barry, author.

Series:

Colloquium publications (American Mathematical Society) ; Volume 54, Part 1.

Colloquium Publications ; Volume 54, Part 1

Language:

English

Subjects (All):

Orthogonal polynomials.

Physical Description:

1 online resource (496 pages) : illustrations.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2005.

Summary:

This two-part book is 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.

Notes:

Includes bibliographical references and indexes.

Description based on online resource; title from PDF title page (ebrary, viewed April 11, 2017).

ISBN:

1-4704-3199-8