General Franklin systems as bases in $H^1[0,1]$
Volume 167 / 2005
Studia Mathematica 167 (2005), 259-292
MSC: 42C10, 46E30.
DOI: 10.4064/sm167-3-7
Abstract
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 $H^1[0,1]$.
