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Approximation by weighted polynomials in ${\Bbb R}^k$

Tom 85 / 2005

Maritza M. Branker Annales Polonici Mathematici 85 (2005), 261-279 MSC: Primary 32U35; Secondary 41A10. DOI: 10.4064/ap85-3-7

Streszczenie

We apply pluripotential theory to establish results in $\mathbb R^k$ concerning uniform approximation by functions of the form $w^n P_n$ where $w$ denotes a continuous nonnegative function and $P_n$ is a polynomial of degree at most $n$. Then we use our work to show that on the intersection of compact sections ${\mit\Sigma} \subset \mathbb R^k$ a continuous function on ${\mit\Sigma}$ is uniformly approximable by $\theta$-incomplete polynomials (for a fixed $\theta,$ $0< \theta < 1$) iff $f$ vanishes on $\theta^2 {\mit\Sigma}$. The class of sets ${\mit\Sigma}$ expressible as the intersection of compact sections includes the intersection of a symmetric convex compact set with a single orthant.

Autorzy

  • Maritza M. BrankerDepartment of Mathematics
    University of Toronto
    Toronto, Canada M5S 3G3
    e-mail

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