Szeg s Theorem and Its Descendants is popular PDF and ePub book, written by Barry Simon in 2010-11-08, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Szeg s Theorem and Its Descendants can be Read Online from any device for your convenience.
Szeg s Theorem and Its Descendants Book PDF Summary
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.
Detail Book of Szeg s Theorem and Its Descendants PDF
- Author : Barry Simon
- Release : 08 November 2010
- Publisher : Princeton University Press
- ISBN : 9781400837052
- Genre : Mathematics
- Total Page : 663 pages
- Language : English
- PDF File Size : 14,9 Mb
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