On the divergence of greedy algorithms with respect to Walsh subsystems in image Original Research Article

In this paper we prove that there exists a function f(x)f(x) which belongs to L1[0,1]L1[0,1] such that a greedy algorithm with respect to the Walsh subsystem does not converge to f(x)f(x) in L1[0,1]L1[0,1] norm, i.e. the Walsh subsystem {Wnk}{Wnk} is not a quasi-greedy basis in its linear span in L1L1.