Computer Mathematics, Mathematical Analysis - Functional Analysis

Orthogonal Polynomials on the Unit Circle : Part 1: Classical Theory; Part 2: Spectral Theory

Name: Orthogonal Polynomials on the Unit Circle : Part 1: Classical Theory; Part 2: Spectral Theory
Author: Barry Simon
ISBN: 9780821837573

by Barry Simon

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Overview

Volume 1 of this two volume set focuses on classical theory. Simon (California Institute of Technology, Pasadena) begins with an introduction to the basic elements of the subject, describing orthogonal polynomials on the real line, Caratheodogy and Schur functions, operator and spectral theory, Verblunsky coefficients, and the Szego recurrence, among other topics. Subsequent chapters delve at length in Szego's theorem, tools for Geronimus' theorem, matrix representations, Baxter's theorem, the Strong Szego theorem, Verblunsky coefficients with rapid decay, and the density of zeros. In v.2, on spectral theory, chapter topics include Rakhmanov's theorem, techniques of spectral analysis, periodic Verblunsky coefficients, spectral analysis of specific classes of Verblunsky coefficients, and the connection to Jacob matrices. Both volumes include a bibliography and author and subject indexes. Volume 2 contains appendices that include a reader's guide to topics and formulae, a discussion of the differences between orthogonal polynomials on a unit circle and those on a real line, a list of conjectures and open questions, and an annotated list of significant papers. Annotation ©2004 Book News, Inc., Portland, OR