Approximation by Müntz spaces on positive intervals

Rachid Ait-Haddou (1) , Marie-Laurence Mazure (2)

1 Geometric Modeling and Scientific Visualization Center
2 MGMI - Modélisation Géométrique & Multirésolution pour l'Image

The so-called Bernstein operators were introduced by S.N. Bernstein in 1912 to give a constructive proof of Weierstrass' theorem. We show how to extend his result to Müntz spaces on positive intervals.

Mots clés: Bernstein bases; Extended Chebyshev spaces; Müntz spaces; Bernstein-type operators; Bernstein bases.

Domaines: Analyse numérique [math.NA]

Rachid Ait-Haddou, Marie-Laurence Mazure. Approximation by Müntz spaces on positive intervals. Comptes Rendus. Mathématique, 2013, 351 (21-22), pp.849-852. ⟨10.1016/j.crma.2013.10.018⟩. ⟨hal-00983519⟩