Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights

• Main Authors: Levin, Eli (Author, http://id.loc.gov/vocabulary/relators/aut), Lubinsky, Doron S. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: SpringerBriefs in Mathematics,
• Subjects: Algebra.; Field theory (Physics).; Approximation theory.; Field Theory and Polynomials.; Approximations and Expansions.

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...

Table of Contents:

• 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.