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.
Зміст
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.
Про автора
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.
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