On greedy algorithms with respect to generalized Walsh system

Details On greedy algorithms with respect to generalized Walsh system On greedy algorithms with respect to generalized Walsh system

2011-09-17

arxiv.org/abs/1109.3806v1

Mathematics

Functional Analysis

Scientific paper

In this paper we proof that there exists a function f(x) belongs to L^1[0,1]
such that a greedy algorithm with regard to generalized Walsh system does not
converge to f(x) in L^1[0,1] norm, i.e. the generalized Walsh system is not a
quasi-greedy basis in its linear span L^1[0,1].

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