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Unconditionality of general Franklin systems in $L^p[0,1]$, $1< p< \infty $

Volume 164 / 2004

Gegham G. Gevorkyan, Anna Kamont Studia Mathematica 164 (2004), 161-204 MSC: 42C10, 46E30. DOI: 10.4064/sm164-2-4

Abstract

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 $L^p[0,1]$, $1< p< \infty$.

Authors

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

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