On the completeness of the system { t λ n log m n t } in C 0 ( E )

Xiangdong Yang

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 2, page 361-379
  • ISSN: 0011-4642

Abstract

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Let E = ⋃ n = 1 ∞ 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 < ⋯ < b n < ⋯ , lim n → ∞ b n = ∞ . Let α ( t ) be a nonnegative function and { λ n } n = 1 ∞ a sequence of distinct complex numbers. In this paper, a theorem on the completeness of the system { t λ n log m n t } 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 ) e - α ( t ) vanishing at infinity.

How to cite

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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 -

References

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