Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights

Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights

SpringerBriefs in Mathematics

von: Eli Levin, Doron S. Lubinsky

55,92 €

Verlag: Springer
Format: PDF
Veröffentl.: 13.02.2018
ISBN/EAN: 9783319729473
Sprache: englisch

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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 topicProvides a general treatment of varying exponential weightsAppeals to a wide range of researchers as well as young mathematicians

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