Homogeneous polynomial approximation on convex and star like domains

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.

Kroó A. (2023) "Homogeneous polynomial approximation on convex and star like domains " Dolomites Research Notes on Approximation, 16(1), 1-9. DOI: 10.14658/PUPJ-DRNA-2023-1-1  
Year of Publication
2023
Journal
Dolomites Research Notes on Approximation
Volume
16
Issue Number
1
Start Page
1
Last Page
9
Date Published
01/2023
ISSN Number
2035-6803
Serial Article Number
1
DOI
10.14658/PUPJ-DRNA-2023-1-1
Issue
Section
Articles