A Weierstrass-type theorem for homogeneous polynomials

DOI10.1090/S0002-9947-08-04625-4zbMath1180.41005arXivmath/0510367OpenAlexW2131818430MaRDI QIDQ3617628

David Benko, András Kroó

Publication date: 30 March 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0510367

zbMATH Keywords

uniform approximationhomogeneous polynomials

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Approximation by polynomials (41A10) Convex sets in (2) dimensions (including convex curves) (52A10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

Density of bivariate homogeneous polynomials on non-convex curves ⋮ Smooth equilibrium measures and approximation ⋮ Rate of approximation of regular convex bodies by convex algebraic level surfaces ⋮ Weighted approximation for weak convex external fields ⋮ Approximation by homogeneous polynomials ⋮ Jackson-type theorems in homogeneous approximation ⋮ Symmetric Liapunov center theorem ⋮ Density of multivariate homogeneous polynomials on star like domains ⋮ Best approximation of functions by log-polynomials ⋮ Weierstrass type approximation by weighted polynomials in \(\mathbb{R}^d\)

Cites Work

• On the support of the equilibrium measure for arcs of the unit circle and for real intervals
• Weighted approximation with varying weight
• Weighted polynomial approximation for convex external fields
• Approximation by weighted polynomials
• A note on weighted polynomial approximation with varying weights
• Approximation by homogeneous polynomials
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