<p>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.</p>

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

Science & Math

BARRY SIMON

Mathematics

American Mathematial Society

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Books by American Mathematial Society

See the best price to sell, buy or rent books by the American Mathematial Society publisher. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

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