Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights [electronic resource] / by Eli Levin, Doron S. Lubinsky
- SpringerBriefs in Mathematics, 2191-8198
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- 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.
- 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. .
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