TY  - BOOK
AU  - Simon, Barry
TI  - Orthogonal polynomials on the unit circle : : Part 2- Spectral Theory
SN  - 9780821848647
AV  - QA1 
PY  - 2009///]
CY  - USA
PB  - AMS
N1  - Chapter 1: The Basics
Chapter 2: Szego's Theorem
Chapter 3: Tools for Geronimus' Theorem
Chapter 4: Matrix Representations
Chapter 5: Baxter's Theorem
Chapter 6: The Strong Szego Theorem
Chapter 7: Verblunsky Coefficients With Rapid Decay
Chapter 8: The Density of Zeros

Part 2 : Spectral Theory
Chapter 9. Rakhmanov’s theorem and related issues
Chapter 10. Techniques of spectral analysis
Chapter 11. Periodic Verblunsky coefficients
Chapter 12. Spectral analysis of specific classes of Verblunsky coefficients
Chapter 13. The connection to Jacobi matrices

N2  - 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 (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
ER  -