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Inequalities for Polynomials With Weights Having Infinitely many Zeros on the Real Line

  • József Szabados
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 142)

Abstract

We prove infinite-finite range, as well as Bernstein—Markov type inequalities for generalized algebraic polynomials on the real line when the weight is the product of a Freud-type weight and of another function which has infinitely many roots on the real line. This kind of investigation is an analogue of the so-called genralized Jacobi weights on finite intervals.

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References

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    P. Borwein and T. Erdélyi, Polynomials and Polynomial Inequalities, Springer Verlag (New York, 1995 ).zbMATHCrossRefGoogle Scholar
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    G. Freud, Orthogonal Polynomials, Akadémiai Kiadó (Budapest, 1971 ).Google Scholar
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    A.L. Levin and D.S. Lubinsky, Orthogonal Polynomials for Exponential Weights, Springer (2001).zbMATHCrossRefGoogle Scholar
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    A.L. Levin and D.S. Lubinsky, Christoffel functions, orthogonal polynomials, and Nevai’s conjecture for Freud weights, Constr. Approx., 8 (1992), 463–535.zbMATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel 2002

Authors and Affiliations

  • József Szabados
    • 1
  1. 1.Afréd Rényi Institute of MathematicsBudapestHungary

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