Addendum to "Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105-109)
Aydin Sh. Shukurov
Colloquium Mathematicae, Tome 135 (2014), p. 297-298 / Harvested from The Polish Digital Mathematics Library
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It is well known that if φ(t) ≡ t, then the system φⁿ(t)n=0∞ is not a Schauder basis in L₂[0,1]. It is natural to ask whether there is a function φ for which the power system φⁿ(t)n=0∞ is a basis in some Lebesgue space Lp. The aim of this short note is to show that the answer to this question is negative.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:284188 
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     title = {Addendum to "Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105-109)},
     journal = {Colloquium Mathematicae},
     volume = {135},
     year = {2014},
     pages = {297-298},
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Aydin Sh. Shukurov. Addendum to "Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105-109). Colloquium Mathematicae, Tome 135 (2014) pp. 297-298. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm137-2-12/