Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights, 1st ed. 2018 SpringerBriefs in Mathematics Series

Langue : Anglais

Auteurs : Levin Eli, Lubinsky Doron S.

Couverture de l’ouvrage Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights

Résumé
Sommaire
Biographie
Commentaire

This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals. Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics.

This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices.

Introduction.- Statement of Main Results.- Potential Theoretic Estimates.- Restricted Range Inequalities.- Bounds for Christoffel Functions.- Spacing of Zeros.- Bounds on Orthogonal Polynomials.- Markov-Bernstein Inequalities in L.- Discretization of Potentials.- Derivatives of Discretized Polynomials.- Weighted Polynomial Approximations.- Formulae Involving Bernstain-Szego Polynomials.- Asymptotics of Orthonormal Polynomials.- Further Bounds.- Universality Limits and Entropy Integrals.

Eli Levin is an emeritus professor at the Open University of Israel in Ramat Aviv.

Doron Lubinsky is a professor at Georgia Institute of Technology. Both are authors of papers on approximation theory, and a joint monograph on orthogonal polynomials.

One of the first books of its kind published on the topic

Provides a general treatment of varying exponential weights

Appeals to a wide range of researchers as well as young mathematicians