ENGLISH

Orthogonal Polynomials on the Unit Circle: Part 1: Classical Theory

By Barry Simon

Book information

Publisher
American Mathematial Society
Year
2009
ISBN
0821848631, 9780821848630
Language
english
Format
PDF
Filesize
27 MB (27910688 bytes)
Series
Colloquium Publications 54
Pages
C, xxvi, 466, B\494
DPI
600
Orientation
portrait
Paginated
yes
Scanned
yes
Time added
2014-12-18 18:00:22

Description

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 (Szegő'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. Readership: Graduate students and research mathematicians interested in analysis.

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