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Szego's Theorem and Its Descendants

Name: Szego's Theorem and Its Descendants
Brand: Princeton University Press
SKU: 04424194
Price: 207.23 EUR
Availability: InStock
Author: Barry Simon
ISBN: 9780691147048

Barry Simon

Jezik

Engleski

Knjiga Tvrdi uvez

Libristo kod: 04424194

Nakladnici Princeton University Press, studeni 2010

This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogo... Cijeli opis

Libristo kod: 04424194

504 b

207.23 €

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