On the completeness of the system $\{t^{{\lambda }_n}{\log }^{m_n}t\}$ in $C_0(E)$

Yang, Xiangdong

Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 361-379.

Résumé

Let $E=\bigcup _{n=1}^{\mathrm{\infty }}{I}_n$ be the union of infinitely many disjoint closed intervals where $I_n=[a_n$, $b_n]$, $0$, $\underset{n\to \mathrm{\infty }}{lim}{b}_n=\mathrm{\infty }.$ Let $\alpha (t)$ be a nonnegative function and $\{{\lambda }_n{\}}_{n=1}^{\mathrm{\infty }}$ 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 $f(t){\mathrm{e}}^{-\alpha (t)}$ vanishing at infinity.

Détail

DOI : 10.1007/s10587-012-0035-4

Classification : 30B60, 30E10, 41A10
Mots-clés : completeness; Banach space; complex Müntz theorem