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Orthogonal Polynomials on the Unit Circle: Spectral theory
Barry Simon
出版American Mathematical Soc., 2005
主題Mathematics / GeneralMathematics / CalculusMathematics / Mathematical Analysis
ISBN08218367579780821836750
URLhttp://books.google.com.hk/books?id=RS9SwzwnZJEC&hl=&source=gbs_api
EBookSAMPLE
註釋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 Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegö'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.