General Franklin system as a basis in $B^1[0,1]$

G. G. Gevorkyan

Yerevan State University

Abstract: For a general Franklin system $\{f_n\}_{n=0}^{\infty}$ generated by an admissible sequence $\mathcal T$, we obtain necessary and sufficient conditions on $\mathcal T$ under which the corresponding system is a basis or an unconditional basis in $B^1[0,1]$.

Keywords: general Franklin system, basis, unconditional basis, spaces $B^1$, $H^1$.

UDC: 517.51

MSC: 41A15, 42C10, 46E30

Received: 09.10.2013
Revised: 04.04.2014

DOI: 10.4213/im8174

 English version: Izvestiya: Mathematics, 2014, 78:6, 1120–1137

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