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Szegő's Theorem and Its Descendants: Spectral Theory for L^2 Perturbations of Orthogonal Polynomials

Simon, Barry (2010) Szegő's Theorem and Its Descendants: Spectral Theory for L^2 Perturbations of Orthogonal Polynomials. Princeton University Press , Princeton, NJ. ISBN 9780691147048. http://resolver.caltech.edu/CaltechAUTHORS:20180808-092107298

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Abstract

This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.


Item Type:Book
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https://press.princeton.edu/titles/9377.htmlPublisherBook Publisher
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 2011 Princeton University Press.
Record Number:CaltechAUTHORS:20180808-092107298
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180808-092107298
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88649
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Aug 2018 17:19
Last Modified:08 Aug 2018 17:19

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