Geodesic
Addendum to “Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105–109)
Aydin Sh. Shukurov1
1 Institute of Mathematics and Mechanics NAS of Azerbaijan Az1141, F. Agayev 9 Baku, Azerbaijan and Baku State University Baku, Azerbaijan
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.
DOI : 10.4064/cm137-2-12
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

Aydin Sh. Shukurov 1

1 Institute of Mathematics and Mechanics NAS of Azerbaijan Az1141, F. Agayev 9 Baku, Azerbaijan and Baku State University Baku, Azerbaijan 
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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. http://geodesic.mathdoc.fr/articles/10.4064/cm137-2-12/

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