Constructive Approximation

, Volume 26, Issue 3, pp 317–337

Approximation by Homogeneous Polynomials


DOI: 10.1007/s00365-006-0639-2

Cite this article as:
Varju, P. Constr Approx (2007) 26: 317. doi:10.1007/s00365-006-0639-2


Let \(K\subset\mathbb{R}^d\) be the boundary of a convex domain symmetric to the origin. The conjecture that any continuous even function can be uniformly approximated by homogeneous polynomials of even degree on K is proven in the following cases: (a) if d = 2; (b) if K is twice continuously differentiable and has positive curvature in every point; or (c) if K is the boundary of a convex polytope.

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© Springer 2006

Authors and Affiliations

  1. 1.Bolyai Institute, SzegedAradi v. tere 1, 6720Hungary