Geodesic
General Franklin systems as bases in $H^1[0,1]$
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
Studia Mathematica, Tome 167 (2005) no. 3, pp. 259-292 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $H^1[0,1]$.
DOI : 10.4064/sm167-3-7
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

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. 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

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