By Barry Simon
This publication provides a accomplished evaluate of the sum rule method of spectral research of orthogonal polynomials, which derives from Gábor Szego's vintage 1915 theorem and its 1920 extension. Barry Simon emphasizes useful and enough stipulations, and gives mathematical historical past that before has been to be had merely in journals. themes comprise heritage from the idea of meromorphic features on hyperelliptic surfaces and the learn of overlaying maps of the Riemann sphere with a finite variety of slits got rid of. this permits for the 1st book-length therapy of orthogonal polynomials for measures supported on a finite variety of periods at the actual line.
as well as the Szego and Killip-Simon theorems for orthogonal polynomials at the unit circle (OPUC) and orthogonal polynomials at the genuine line (OPRL), Simon covers Toda lattices, the instant challenge, and Jacobi operators at the Bethe lattice. contemporary paintings on functions of universality of the CD kernel to acquire particular asymptotics at the high-quality constitution of the zeros is usually incorporated. The ebook locations targeted emphasis on OPRL, which makes it the basic better half quantity to the author's past books on OPUC.
Read or Download Szegő's Theorem and Its Descendants: Spectral Theory for L2 Perturbations of Orthogonal Polynomials (Porter Lectures) PDF
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