On the completeness of the system $\{t^{\lambda _{n}}\log ^{m_{n}}t\}$ in $C_{0}(E)$

Title:

On the completeness of the system $\{t^{\lambda _{n}}\log ^{m_{n}}t\}$ in $C_{0}(E)$

Creator:

Xiangdong

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:f9afa4e7-909c-484b-b7b8-77bc8821f1f3
uuid:f9afa4e7-909c-484b-b7b8-77bc8821f1f3

Subject:

completeness, Banach space, and complex Müntz theorem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 $\{\lambda _{n}\}_{n=1}^{\infty }$ a sequence of distinct complex numbers. In this paper, a theorem on the completeness of the system $\{t^{\lambda _{n}}\log ^{m_{n}}t\}$ in $C_{0}(E)$ is obtained where $C_{0}(E)$ is the weighted Banach space consists of complex functions continuous on $E$ with $f(t){\rm e}^{-\alpha (t)}$ vanishing at infinity.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

361-379

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:2

Harvested from:

CDK

Metadata only:

false