Orthogonal Polynomials for Exponential Weights (Relié)

Doron-S Lubinsky, Eli Levin

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  • Springer

  • Paru le : 09/08/2001
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The analysis of orthogonal polynomials associated with general weights was a major theme in classical analysis in the twentieth century and undoubtedly will continue to grow in importance in the future. In this monograph, the authors investigate orthogonal polynomials for exponential weights defined on a finite or infinite interval. The interval should contain 0, but need not be symmetric about 0 ; likewise, the weight need not be even. The authors establish bounds and asymptotics for orthonormal and extremal polynomials, and their associated Christoffel functions. They deduce bounds on zeros of extremal and orthogonal polynomials, and also establish Markov-Bernstein and Nikolskii inequalities. The book will be of interest to researchers in approximation theory, harmonic analysis, numerical analysis, potential theory, and all those that apply orthogonal polynomials.
    • Introduction and Results
    • Weighted Potential Theory : The Basics
    • Basic Estimate for Q, at
    • Restricted Range Inequalities
    • Estimates for Measure and Potential
    • Smoothness of (t
    • Weighted Polynomial Approximation
    • Asymptotics of Extremal Errors
    • Christoffel Functions
    • Markov-Bernstein and Nikolskii Inequalities
    • Zeros of Orthogonal Polynomials
    • Bounds on Orthogonal Polynomials
    • Further Bounds and Applications
    • Asymptotics of Extremal Polynomials
    • Asymptotics of Orthonormal Polynomials
Eli (A.L.) Levin received a Ph.D. degree in mathematics from Moscow State University in 1970. In 1979 he joined the Faculty of the Open University of Israel in Tel Aviv, where he is currently Associate Professor. Doron S. Lubinsky received a Ph.D. degree from Witwatersrand University, Johannesburg, South Africa, in 1981. In 1989 he joined the faculty of Witwatersrand University where he is currently Full Professor.

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