[Banach] Abstract of a paper by S. J. Dilworth, S. Gogyan, and Denka Kutzarova

This is an announcement for the paper "On the convergence of a weak greedy algorithm for the multivariate Haar basis" by S. J. Dilworth, S. Gogyan, and Denka Kutzarova.

Abstract: We define a family of weak thresholding greedy algorithms for the multivariate Haar basis for $L_1[0,1]^d$ ($d \ge 1$). We prove convergence and uniform boundedness of the weak greedy approximants for all $f \in L_1[0,1]^d$.

Archive classification: math.FA math.CA

Mathematics Subject Classification: Primary: 41A65. Secondary: 42A10, 46B20

Remarks: 25 pages

Submitted from: dilworth@math.sc.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1209.1378

or

http://arXiv.org/abs/1209.1378