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008			190301b ||||| |||| 00| 0 eng d
020			_a9780821848630
040			_cEducational Supplies _aICTS-TIFR
050			_aQA1
100			_aSimon, Barry
245			_aOrthogonal polynomials on the unit circle _b: Part 1- Classical Theory
250			_aVol. 54
260			_aUSA: _bAMS, _c[c2009]
300			_a496 p
505			_aChapter 1. The Basics Chapter 2. Szegő’s theorem Chapter 3. Tools for Geronimus’ theorem Chapter 4. Matrix representations Chapter 5. Baxter’s theorem Chapter 6. The strong Szegő theorem Chapter 7. Verblunsky coefficients with rapid decay Chapter 8. The density of zeros
520			_aThis 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
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