Constructive Characteristic of ho¨ Lder Classes and M-Term Approximations in the Multiple Haar Basis

Abstract

In terms of the best polynomial approximations in the multiple Haar basis, we obtain a constructive characteristic of the Holder classes H of functions defined on the unit cube $$ \mathbb{I} $$ d of the space ℝ d under the restriction $$ 0<\alpha <\frac{1}{p}\le 1 $$ . We also solve the problem of order estimates of the best m-term approximations in the Haar basis of classes H in the Lebesgue spaces L q ( $$ \mathbb{I} $$ d ).