Global Journal of Pure and Applied Mathematics
  • Year: 2007
  • Volume: 3
  • Issue: 1

On Greedy Algorithms with Respect to Generalized Walsh System

  • Author:
  • S.A. Episkoposian
  • Total Page Count: 10
  • Page Number: 37 to 46

Department of Physics, State University of Yerevan, Alex Manukian 1, 375049 Yerevan, Armenia. E-mail: sergoep@ysu.am

AMS Subject Classification: Primary 42C10, Secondary 46E30.

Abstract

In this paper we proof that there exists a function f (x) belongs to L1[0, 1] such that a greedy algorithm with regard to generalized Walsh system does not converge to f (x) in L1[0, 1] norm, i.e. the generalized Walsh system is not a quasi-greedy basis in its linear span L1[0, 1].

Keywords

Greedy algorithms, generalized Walsh system, quasi-greedy basis