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Szego's Theorem and Its Descendants - Spectral Theory for L2 Perturbations of Orthogonal Polynomials (Electronic book text)
Szego's Theorem and Its Descendants - Spectral Theory for L2 Perturbations of Orthogonal Polynomials (Electronic book...
Szego's Theorem and Its Descendants - Spectral Theory for L2 Perturbations of Orthogonal Polynomials (Electronic book...

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Szego's Theorem and Its Descendants - Spectral Theory for L2 Perturbations of Orthogonal Polynomials (Electronic book text)

Barry Simon

Series: Porter Lectures

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This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gabor 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.

General

Imprint: Princeton University Press
Country of origin: United States
Series: Porter Lectures
Release date: 2011
First published: 2011
Authors: Barry Simon
Format: Electronic book text
Pages: 664
ISBN-13: 978-1-4008-3705-2
Barcode: 9781400837052
Categories: Promotions
Books
LSN: 1-4008-3705-7

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