Orthogonal Polynomials on the Unit Circle: Spectral theory, Part 2
Presents an overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. This book discusses topics such as asymptotics of Toeplitz determinants (Szego's theorems), and limit theorems for the density of the zeros of orthogonal polynomials.
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Preface to Part 1
Rakhmanovs Theorem and Related Issues
Techniques of Spectral Analysis
The Basics 1
Periodic Verblunsky Coefficients
Spectral Analysis of Specific Classes
The Connection to Jacobi Matrices
analog analytic apply argument associated asymptotics bands bounded called Caratheodory function Cited closed common compact complete condition constant continuous convergence Corollary define Definition dense determines direct Dirichlet data discuss eigenvalues equation equivalent Example exists extended fact finite fixed follows formula given holds ideas implies independent integral interval invariant Lemma limit matrix minimal Moreover multiplicity nontrivial probability measure obeys OPRL OPUC particular periodic perturbations Pick poles polynomial positive Proof of Theorem Proposition prove pure point ratio Remarks replaced result root says Schrodinger operators Schur Section sequence shows side simple singular solution spectral spectrum subsets Suppose Szego theory uniformly unique values Verblunsky coefficients write zeros