Geodesic
On the completeness of the system $\{t^{\lambda _{n}}\log ^{m_{n}}t\}$ in $C_{0}(E)$
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 361-379

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Let $E=\bigcup _{n=1}^{\infty }I_{n}$ be the union of infinitely many disjoint closed intervals where $I_{n}=[a_{n}$, $b_{n}]$, $0$, $\lim _{n\rightarrow \infty }b_{n}=\infty .$ 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.
DOI : 10.1007/s10587-012-0035-4
Classification : 30B60, 30E10, 41A10
Keywords: completeness; Banach space; complex Müntz theorem 
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     title = {On the completeness of the system $\{t^{\lambda _{n}}\log ^{m_{n}}t\}$ in $C_{0}(E)$},
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Yang, Xiangdong. On the completeness of the system $\{t^{\lambda _{n}}\log ^{m_{n}}t\}$ in $C_{0}(E)$. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 361-379. doi: 10.1007/s10587-012-0035-4

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