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.
| ISBN: | 9780821848647 |
| Publication date: | 30th December 2013 |
| Author: | Barry Simon |
| Publisher: | American Mathematical Society |
| Format: | Paperback |
| Pagination: | 578 pages |
| Series: | Colloquium Publications |
| Genres: |
Probability and statistics Calculus and mathematical analysis |
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.
Orthogonal Polynomials on the Unit Circle features in the following genres: Probability and statistics, Calculus and mathematical analysis
Orthogonal Polynomials on the Unit Circle is available in Paperback
Orthogonal Polynomials on the Unit Circle was written by Barry Simon and published by American Mathematical Society
Orthogonal Polynomials on the Unit Circle has 578 pages
Yes it is part of Colloquium Publications series