Approximation by weighted polynomials in $ℝ^k$

• Autorzy: Maritza M. Branker
• Języki publikacji: EN

Abstrakty

EN

We apply pluripotential theory to establish results in $ℝ^k$ concerning uniform approximation by functions of the form wⁿPₙ where w denotes a continuous nonnegative function and Pₙ is a polynomial of degree at most n. Then we use our work to show that on the intersection of compact sections $Σ ⊂ ℝ^k$ a continuous function on Σ is uniformly approximable by θ-incomplete polynomials (for a fixed θ, 0 < θ < 1) iff f vanishes on θ²Σ. The class of sets Σ expressible as the intersection of compact sections includes the intersection of a symmetric convex compact set with a single orthant.

Kategorie tematyczne

• 32U35: Pluricomplex Green functions
• 41A10: Approximation by polynomials

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2005
• Tom: 85
• Numer: 3
• Strony: 261-279

Daty

wydano

2005

Twórcy

autor

Maritza M. Branker

• Department of Mathematics, University of Toronto, Toronto, Canada M5S 3G3

Identyfikatory

DOI

10.4064/ap85-3-7