Orthogonal Polynomials on the Unit Circle: Spectral Theory Part 2 (Colloquium Publications): Part 2: Spectral Theory - Softcover

Simon, Barry

 
9780821848647: Orthogonal Polynomials on the Unit Circle: Spectral Theory Part 2 (Colloquium Publications): Part 2: Spectral Theory
Softcover
ISBN 10: 082184864X ISBN 13: 9780821848647
Publisher: American Mathematical Society, 2013

Synopsis

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.

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About the Author

Barry Simon, California Institute of Technology, Pasadena, CA, USA

"About this title" may belong to another edition of this title.

Publisher
American Mathematical Society
Publication date
2013
Language
English
ISBN 10 
082184864X
ISBN 13 
9780821848647
Binding
Paperback
Number of pages
578