By a general Franklin system corresponding to a dense sequence of knots 𝓣 = (tₙ, n ≥ 0) in [0,1] we mean a sequence of orthonormal piecewise linear functions with knots 𝓣, that is, the nth function of the system has knots t₀, ..., tₙ. The main result of this paper is a characterization of sequences 𝓣 for which the corresponding general Franklin system is a basis or an unconditional basis in H¹[0,1].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm167-3-7,
author = {Gegham G. Gevorkyan and Anna Kamont},
title = {General Franklin systems as bases in H$^1$[0,1]},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {259-292},
zbl = {1073.42018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm167-3-7}
}
Gegham G. Gevorkyan; Anna Kamont. General Franklin systems as bases in H¹[0,1]. Studia Mathematica, Tome 166 (2005) pp. 259-292. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm167-3-7/