Szego's Theorem and Its Descendants: Spectral Theory for L2 Perturbations of Orthogonal Polynomials (BOK)

Barry Simon

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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.


Språk Engelsk Engelsk Innbinding Heftet
Utgitt 2010 Forfatter Barry Simon
University Press Group Ltd
ISBN 9780691147048
Antall sider 664 Dimensjoner 15,2cm x 22,9cm x 3,8cm
Vekt 1085 gram Leverandør Bertram Trading Ltd
Emner og form Mathematics, Quantum physics (quantum mechanics & quantum field theory)