Szegő’s Theorem and Its Descendants: Spectral Theory for L² Perturbations of Orthogonal Polynomials (Porter Lectures Book 6) by Barry Simon (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐

⭐

⭐

Keywords

Free Download Szegő’s Theorem and Its Descendants: Spectral Theory for L² Perturbations of Orthogonal Polynomials (Porter Lectures Book 6) in PDF format
Szegő’s Theorem and Its Descendants: Spectral Theory for L² Perturbations of Orthogonal Polynomials (Porter Lectures Book 6) PDF Free Download
Download Szegő’s Theorem and Its Descendants: Spectral Theory for L² Perturbations of Orthogonal Polynomials (Porter Lectures Book 6) 2010 PDF Free
Szegő’s Theorem and Its Descendants: Spectral Theory for L² Perturbations of Orthogonal Polynomials (Porter Lectures Book 6) 2010 PDF Free Download
Download Szegő’s Theorem and Its Descendants: Spectral Theory for L² Perturbations of Orthogonal Polynomials (Porter Lectures Book 6) PDF
Free Download Ebook Szegő’s Theorem and Its Descendants: Spectral Theory for L² Perturbations of Orthogonal Polynomials (Porter Lectures Book 6)