Szegő's Theorem and Its Descendants

Spectral Theory for L2 Perturbations of Orthogonal Polynomials

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Science, Physics, Mathematical Physics
Cover of the book Szegő's Theorem and Its Descendants by Barry Simon, Princeton University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Barry Simon ISBN: 9781400837052
Publisher: Princeton University Press Publication: November 8, 2010
Imprint: Princeton University Press Language: English
Author: Barry Simon
ISBN: 9781400837052
Publisher: Princeton University Press
Publication: November 8, 2010
Imprint: Princeton University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Princeton University Press

Cover of the book Cities of Knowledge by Barry Simon
Cover of the book The Darwin Economy: Liberty, Competition, and the Common Good by Barry Simon
Cover of the book The Emergence of Organizations and Markets by Barry Simon
Cover of the book Computational Aspects of Modular Forms and Galois Representations by Barry Simon
Cover of the book Our Minds, Our Selves by Barry Simon
Cover of the book The Nobel Factor by Barry Simon
Cover of the book The Modern Art of Dying by Barry Simon
Cover of the book Kierkegaard's Writings, XI, Volume 11 by Barry Simon
Cover of the book Straight Talk on Trade by Barry Simon
Cover of the book Augustine's Confessions by Barry Simon
Cover of the book Kierkegaard's Writings, V, Volume 5 by Barry Simon
Cover of the book The Essential Hirschman by Barry Simon
Cover of the book The Shape of the New by Barry Simon
Cover of the book The Secular City by Barry Simon
Cover of the book Currency Power by Barry Simon
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy