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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## General Franklin systems as bases in $H^1[0,1]$

### Tom 167 / 2005

Studia Mathematica 167 (2005), 259-292 MSC: 42C10, 46E30. DOI: 10.4064/sm167-3-7

#### Streszczenie

By a general Franklin system corresponding to a dense sequence of knots ${\cal T}=(t_n, n \geq 0)$ in $[0,1]$ we mean a sequence of orthonormal piecewise linear functions with knots ${\cal T}$, that is, the $n$th function of the system has knots $t_0, \ldots, t_n$. The main result of this paper is a characterization of sequences ${\cal T}$ for which the corresponding general Franklin system is a basis or an unconditional basis in $H^1[0,1]$.

#### Autorzy

• Gegham G. GevorkyanDepartment of Mathematics
Yerevan State University
Alex Manoukian St. 1
375049 Yerevan, Armenia
e-mail
• Anna KamontInstitute of Mathematics