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Weighted Polynomial Approximation for Weights with Logarithmic Singularities in the Extremal Measure

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Abstract

Let w : Σ → [0, ∞) be a weight function on a set Σ ⊂ R. We assume that the associated extremal measure μω has density function vω(t) with finitely many singularities of logarithmic type. We show that any continuous function f on Σ which vanishes outside the set where vω is positive or has a logarithmic singularity, is the uniform limit on Σ of a sequence of weighted polynomials of the form wn Pn, where Pn is of degree ≦ n. This extends previous results for continuous densities to densities having logarithmic singularities.

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Authors and Affiliations

  1. Department of Mathematics, University of South Florida, Tampa, FL, 33620-5700, U.S.A.

    P. C. Simeonov

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  1. P. C. Simeonov
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Simeonov, P.C. Weighted Polynomial Approximation for Weights with Logarithmic Singularities in the Extremal Measure. Acta Mathematica Hungarica 82, 265–296 (1999). https://doi.org/10.1023/A:1006632024030

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