a sequence of distinct complex numbers. In this paper, a theorem on the completeness of the system
is obtained where
is the weighted Banach space consists of complex functions continuous on
vanishing at infinity.
How to cite
Yang, Xiangdong. "On the completeness of the system $\lbrace t^{\lambda _{n}}\log ^{m_{n}}t\rbrace $ in $C_{0}(E)$."
Czechoslovak Mathematical Journal
62.2 (2012): 361-379. <http://eudml.org/doc/246485>.
@article{Yang2012,
abstract = {Let $E=\bigcup _\{n=1\}^\{\infty \}I_\{n\}$ be the union of infinitely many disjoint closed intervals where $I_\{n\}=[a_\{n\}$, $b_\{n\}]$, $0<a_\{1\}<b_\{1\}<a_\{2\}<b_\{2\}<\dots <b_\{n\}<\dots $, $\lim _\{n\rightarrow \infty \}b_\{n\}=\infty .$ Let $\alpha (t)$ be a nonnegative function and $\lbrace \lambda _\{n\}\rbrace _\{n=1\}^\{\infty \}$ a sequence of distinct complex numbers. In this paper, a theorem on the completeness of the system $\lbrace t^\{\lambda _\{n\}\}\log ^\{m_\{n\}\}t\rbrace $ in $C_\{0\}(E)$ is obtained where $C_\{0\}(E)$ is the weighted Banach space consists of complex functions continuous on $E$ with $f(t)\{\rm e\}^\{-\alpha (t)\}$ vanishing at infinity.},
author = {Yang, Xiangdong},
journal = {Czechoslovak Mathematical Journal},
keywords = {completeness; Banach space; complex Müntz theorem; completeness; Banach space; complex Müntz theorem},
language = {eng},
number = {2},
pages = {361-379},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the completeness of the system $\lbrace t^\{\lambda _\{n\}\}\log ^\{m_\{n\}\}t\rbrace $ in $C_\{0\}(E)$},
url = {http://eudml.org/doc/246485},
volume = {62},
year = {2012},
}
TY - JOUR
AU - Yang, Xiangdong
TI - On the completeness of the system $\lbrace t^{\lambda _{n}}\log ^{m_{n}}t\rbrace $ in $C_{0}(E)$
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 2
SP - 361
EP - 379
AB - Let $E=\bigcup _{n=1}^{\infty }I_{n}$ be the union of infinitely many disjoint closed intervals where $I_{n}=[a_{n}$, $b_{n}]$, $0<a_{1}<b_{1}<a_{2}<b_{2}<\dots <b_{n}<\dots $, $\lim _{n\rightarrow \infty }b_{n}=\infty .$ Let $\alpha (t)$ be a nonnegative function and $\lbrace \lambda _{n}\rbrace _{n=1}^{\infty }$ a sequence of distinct complex numbers. In this paper, a theorem on the completeness of the system $\lbrace t^{\lambda _{n}}\log ^{m_{n}}t\rbrace $ in $C_{0}(E)$ is obtained where $C_{0}(E)$ is the weighted Banach space consists of complex functions continuous on $E$ with $f(t){\rm e}^{-\alpha (t)}$ vanishing at infinity.
LA - eng
KW - completeness; Banach space; complex Müntz theorem; completeness; Banach space; complex Müntz theorem
UR - http://eudml.org/doc/246485
ER -
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