On the divergence of greedy algorithms with respect to Walsh subsystems in $L$

Sergo A. Episkoposian

On the divergence of greedy algorithms with respect to Walsh subsystems in $L$

Functional Analysis 2015-01-06 v1

Authors: Sergo A. Episkoposian

Abstract

In this paper we prove that there exists a function which $f(x)$ belongs to $L^1[0,1]$ such that a greedy algorithm with regard to the Walsh subsystem does not converge to $f(x)$ in $L^1[0,1]$ norm, i.e. the Walsh subsystem $\{W_{n_k}\}$ is not a quasi-greedy basis in its linear span in $L^1$ .

Keywords

greedy algorithm walsh subsystem quasi-greedy basis l1 space divergence linear span

Cite

@article{arxiv.1501.00832,
  title  = {On the divergence of greedy algorithms with respect to Walsh subsystems in $L$},
  author = {Sergo A. Episkoposian},
  journal= {arXiv preprint arXiv:1501.00832},
  year   = {2015}
}

Comments

appears in Journal of Nonlinear Analysis Series A: Theory, Methods & Applications, 2007

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