eBook - ePub

Szegő's Theorem and Its Descendants

Name: Szegő's Theorem and Its Descendants
Author: Barry Simon

Spectral Theory for L2 Perturbations of Orthogonal Polynomials

Barry Simon,

664 pages
English
ePUB (mobile friendly)
Available on iOS & Android

eBook - ePub

Szegő's Theorem and Its Descendants

Spectral Theory for L2 Perturbations of Orthogonal Polynomials

Barry Simon,

About this book

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.

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Yes, you can access Szegő's Theorem and Its Descendants by Barry Simon in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.