Orthogonal Polynomials on the Unit Circle: Part 2: Spectral Theory (Colloquium Publications)
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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.
Format:Paperback
Language:English
ISBN:082184864X
ISBN13:9780821848647
Release Date:November 2009
Publisher:American Mathematical Society
Length:578 Pages
Weight:2.38 lbs.
Dimensions:10.0" x 7.0"
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