Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights

1. Auflage 2018
ISBN: 978-3-319-72946-6
Verlag: Springer International Publishing

Buch, Englisch, 170 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 283 g

Reihe: SpringerBriefs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Lubinsky, Doron S.

Levin, Eli

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

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.