Inverse theorems for multidimensional Bernstein operators

Zeev Ditzian

Vol. 121 (1986), No. 2, 293–319

DOI: 10.2140/pjm.1986.121.293

Abstract

Let B_nf be the m-dimensional Bernstein polynomials on a simplex or on a cube. The class of functions for which ∥B_nf − f∥ = O(n^−α) is determined. That is, necessary and sufficient conditions on the smoothness of f in the simplex or the cube and especially near their boundaries are given so that ∥B_nf − f∥ = O(n^−α). Interpolation of spaces, and in particular the characterization of the interpolation space, is one of the tools used.

Mathematical Subject Classification 2000

Primary: 41A35

Secondary: 41A25, 41A27

Milestones

Received: 21 November 1983

Published: 1 February 1986