General Franklin systems as bases in $H^1[0,1]$

Volume 167 / 2005

Gegham G. Gevorkyan, Anna Kamont Studia Mathematica 167 (2005), 259-292 MSC: 42C10, 46E30. DOI: 10.4064/sm167-3-7


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 $H^1[0,1]$.


  • Gegham G. GevorkyanDepartment of Mathematics
    Yerevan State University
    Alex Manoukian St. 1
    375049 Yerevan, Armenia
  • Anna KamontInstitute of Mathematics
    Polish Academy of Sciences
    Abrahama 18
    81-825 Sopot, Poland

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