Addendum to “Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces"
(Colloq. Math. 127 (2012), 105–109)
Colloquium Mathematicum, Tome 137 (2014) no. 2, pp. 297-298
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
It is well known that if $\varphi (t) \equiv t $, then the system $ \{ \varphi ^{n}(t)\}_{n=0}^{\infty }$ is not a Schauder basis in $ L_{2}[0,1] $. It is natural to ask whether there is a function $\varphi $ for which the power system $ \{ \varphi ^{n}(t)\}_{n=0}^{\infty }$ is a basis in some Lebesgue space $L_{p}$. The aim of this short note is to show that the answer to this question is negative.
Keywords:
known varphi equiv system varphi infty schauder basis natural ask whether there function varphi which power system varphi infty basis lebesgue space short note answer question negative
Affiliations des auteurs :
Aydin Sh. Shukurov 1
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author = {Aydin Sh. Shukurov},
title = {Addendum to {{\textquotedblleft}Necessary} condition for {Kostyuchenko} type systems to be a basis in {Lebesgue} spaces"
{(Colloq.} {Math.} 127 (2012), 105{\textendash}109)},
journal = {Colloquium Mathematicum},
pages = {297--298},
publisher = {mathdoc},
volume = {137},
number = {2},
year = {2014},
doi = {10.4064/cm137-2-12},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm137-2-12/}
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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 Mathematicum, Tome 137 (2014) no. 2, pp. 297-298. doi: 10.4064/cm137-2-12
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