Addendum to "Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105-109)

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 137.2 (2014): 297-298. <http://eudml.org/doc/284188>.

@article{AydinSh2014,
abstract = {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 $L_\{p\}$. The aim of this short note is to show that the answer to this question is negative.},
author = {Aydin Sh. Shukurov},
journal = {Colloquium Mathematicae},
keywords = {bases; Kostyuchenko system; system of powers},
language = {eng},
number = {2},
pages = {297-298},
title = {Addendum to "Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105-109)},
url = {http://eudml.org/doc/284188},
volume = {137},
year = {2014},
}

TY - JOUR
AU - Aydin Sh. Shukurov
TI - Addendum to "Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105-109)
JO - Colloquium Mathematicae
PY - 2014
VL - 137
IS - 2
SP - 297
EP - 298
AB - 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 $L_{p}$. The aim of this short note is to show that the answer to this question is negative.
LA - eng
KW - bases; Kostyuchenko system; system of powers
UR - http://eudml.org/doc/284188
ER -