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 167 (2005) no. 3, pp. 259-292
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 $H^1[0,1]$.
Keywords:
general franklin system corresponding dense sequence knots cal geq mean sequence orthonormal piecewise linear functions knots cal nth function system has knots ldots main result paper characterization sequences cal which corresponding general franklin system basis unconditional basis
Affiliations des auteurs :
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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author = {Gegham G. Gevorkyan and Anna Kamont},
title = {General {Franklin} systems as bases in $H^1[0,1]$},
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Gegham G. Gevorkyan; Anna Kamont. General Franklin systems as bases in $H^1[0,1]$. Studia Mathematica, Tome 167 (2005) no. 3, pp. 259-292. doi: 10.4064/sm167-3-7
