Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights

✍ Scribed by Eli Levin,Doron S. Lubinsky (auth.)

Publisher: Springer International Publishing
Year: 2018
Tongue: English
Leaves: 168
Series: SpringerBriefs in Mathematics
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-vii
Introduction (Eli Levin, Doron S. Lubinsky)....Pages 1-8
Statement of Main Results (Eli Levin, Doron S. Lubinsky)....Pages 9-12
Potential Theoretic Estimates (Eli Levin, Doron S. Lubinsky)....Pages 13-27
Restricted Range Inequalities (Eli Levin, Doron S. Lubinsky)....Pages 29-35
Bounds for Christoffel Functions (Eli Levin, Doron S. Lubinsky)....Pages 37-45
Spacing of Zeros (Eli Levin, Doron S. Lubinsky)....Pages 47-51
Bounds on Orthogonal Polynomials (Eli Levin, Doron S. Lubinsky)....Pages 53-62
Markov-Bernstein Inequalities in L∞ (Eli Levin, Doron S. Lubinsky)....Pages 63-65
Discretization of Potentials (Eli Levin, Doron S. Lubinsky)....Pages 67-82
Derivatives of Discretized Polynomials (Eli Levin, Doron S. Lubinsky)....Pages 83-92
Weighted Polynomial Approximations (Eli Levin, Doron S. Lubinsky)....Pages 93-115
Formulae Involving Bernstein-Szegő Polynomials (Eli Levin, Doron S. Lubinsky)....Pages 117-122
Asymptotics of Orthonormal Polynomials (Eli Levin, Doron S. Lubinsky)....Pages 123-142
Further Bounds (Eli Levin, Doron S. Lubinsky)....Pages 143-151
Universality Limits and Entropy Integrals (Eli Levin, Doron S. Lubinsky)....Pages 153-164
Back Matter ....Pages 165-170

✦ Subjects

Field Theory and Polynomials

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