# Renormalized Haar system as quasi-greedy basis in $L^1(0,1)$

Smbat Gogyan
Institute of Mathematics, Polish Academy of Sciences
POLAND

given at  strobl07 (21.06.07 09:00)
id:  570
length:  25min
status:  accepted
type:  talk
Let $\{h_n\}$ be the Haar system (normalized in $L^1(0,1)$). We describe all nondecreasing sequences $\omega=\{\omega_n\}$
such that the system $\{\omega_n h_n\}$ is a quasi-greedy basis in
$L^1(0,1)$. We also prove convergence result on Weak Thresholding Greedy Algorithm in $L^1(0,1)$.