Constructive Characteristic of ho¨ Lder Classes and <em class="a-plus-plus">M</em>-Term Approximations in the Multiple Haar Basis

  • V. S. Romanyuk

Abstract

In terms of the best polynomial approximations in the multiple Haar basis, we obtain a constructive characteristic of the Hölder classes H p α 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 p α in the Lebesgue spaces L q ( \( \mathbb{I} \) d ).
Published
25.03.2014
How to Cite
RomanyukV. S. “Constructive Characteristic of Ho¨ Lder Classes and <em class="a-Plus-plus">M</Em&gt;-Term Approximations in the Multiple Haar Basis”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 3, Mar. 2014, pp. 349–360, http://umj.imath.kiev.ua/index.php/umj/article/view/2137.
Section
Research articles