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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Unconditionality of general Franklin systems in $L^p[0,1]$, $1< p< \infty$

### Tom 164 / 2004

Studia Mathematica 164 (2004), 161-204 MSC: 42C10, 46E30. DOI: 10.4064/sm164-2-4

#### Streszczenie

By a general Franklin system corresponding to a dense sequence ${\cal T}=(t_n, n \geq 0)$ of points 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 that each general Franklin system is an unconditional basis in $L^p[0,1]$, $1< p< \infty$.

#### Autorzy

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