Homogeneous polynomial approximation on convex and star like domains
Title | Homogeneous polynomial approximation on convex and star like domains |
Publication Type | Journal Article |
Year of Publication | 2023 |
Authors | Kroó, A |
Journal | Dolomites Research Notes on Approximation |
Volume | 16 |
Issue | 1 |
Pagination | 1-9 |
Date Published | 01/2023 |
Publisher | Padova University Press |
Place Published | Padova, IT |
ISSN Number | 2035-6803 |
Abstract | In the present paper we consider the following central problem on the approximation by homogeneous polynomials: For which 0-symmetric star like domains K ⊂ R d and which f ∈ C(∂ K) there exist homogeneous polynomials hn , hn+1 of degree n and n + 1, respectively, so that uniformly on ∂ K f = limn→∞ (hn + hn+1 )? This question is the analogue of the Weierstrass approximation problem when polynomials of total degree are replaced by the homogeneous polynomials. A survey of various recent results on the above question is given with some relevant open problems being included, as well. |
URL | https://drna.padovauniversitypress.it/2023/1/1 |
DOI | 10.14658/pupj-drna-2023-1-1 |