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

Maritza M. Branker. "Approximation by weighted polynomials in $ℝ^k$." Annales Polonici Mathematici 85.3 (2005): 261-279. <http://eudml.org/doc/280431>.

@article{MaritzaM2005,
abstract = {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.},
author = {Maritza M. Branker},
journal = {Annales Polonici Mathematici},
keywords = {multivariable incomplete polynomials; weighted pluricomplex Green function},
language = {eng},
number = {3},
pages = {261-279},
title = {Approximation by weighted polynomials in $ℝ^k$},
url = {http://eudml.org/doc/280431},
volume = {85},
year = {2005},
}

TY - JOUR
AU - Maritza M. Branker
TI - Approximation by weighted polynomials in $ℝ^k$
JO - Annales Polonici Mathematici
PY - 2005
VL - 85
IS - 3
SP - 261
EP - 279
AB - 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.
LA - eng
KW - multivariable incomplete polynomials; weighted pluricomplex Green function
UR - http://eudml.org/doc/280431
ER -