Geodesic
Unconditionality of general Franklin systems in $L^p[0,1]$, $1 p \infty $
Gegham G. Gevorkyan1 ; Anna Kamont2
1Department of Mathematics Yerevan State University Alex Manoukian St. 1 375049 Yerevan, Armenia
2Institute of Mathematics Polish Academy of Sciences Abrahama 18 81-825 Sopot, Poland
Studia Mathematica, Tome 164 (2004) no. 2, pp. 161-204
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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 $L^p[0,1]$, $1 p \infty$.
DOI : 10.4064/sm164-2-4
Keywords: general franklin system corresponding dense sequence cal geq points mean sequence orthonormal piecewise linear functions knots cal nth function system has knots ldots main result paper each general franklin system unconditional basis infty

Gegham G. Gevorkyan  1   ; Anna Kamont  2

1 Department of Mathematics Yerevan State University Alex Manoukian St. 1 375049 Yerevan, Armenia
2 Institute of Mathematics Polish Academy of Sciences Abrahama 18 81-825 Sopot, Poland 
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Gegham G. Gevorkyan; Anna Kamont. Unconditionality of general Franklin systems
 in $L^p[0,1]$, $1< p< \infty $. Studia Mathematica, Tome 164 (2004) no. 2, pp. 161-204. doi: 10.4064/sm164-2-4

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