Multiple Haar Basis and its Properties

  • V. S. Romanyuk

Abstract

In the Lebesgue spaces $L_p ([0, 1]^d ), 1 ≤ p ≤ ∞$, for $d ≥ 2$, we define a multiple basis system of functions $H^d  = (h_n )_{n = 1}^{∞}$. This system has the main properties of the well-known one-dimensional Haar basis $H$. In particular, it is shown that the system $H^d$ is a Schauder basis in the spaces $L_p ([0, 1]^d ),\; 1 ≤ p < ∞$.
Published
25.09.2015
How to Cite
RomanyukV. S. “Multiple Haar Basis and Its Properties”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 9, Sept. 2015, pp. 1253–1264, http://umj.imath.kiev.ua/index.php/umj/article/view/2063.
Section
Research articles