$L^1$- convergence of greedy algorithm by generalized Walsh system

TL;DR

This paper investigates the $L^1$-convergence of a greedy algorithm based on the generalized Walsh system, focusing on how small modifications to function values affect convergence.

Contribution

It introduces analysis of $L^1$-convergence for a greedy algorithm using the generalized Walsh system with small set modifications.

Findings

Established conditions for $L^1$-convergence of the greedy algorithm.

Analyzed the impact of small set changes on convergence behavior.

Provided theoretical results on convergence stability.

Abstract

In this paper we consider the generalized Walsh system and a problem $L^1- convergence$ of greedy algorithm of functions after changing the values on small set.