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On the completeness of the system \{ {t^{{\lambda _n}}}{\log ^{{m_n}}}t\} in C 0(E)
Authors:Xiangdong Yang
Institution:1. Department of Mathematics, Kunming University of Science and Technology, 650093, Kunming, China
Abstract:Let $E = \bigcup\limits_{n = 1}^\infty {{I_n}} $ be the union of infinitely many disjoint closed intervals where In = a n , b n ], 0 < a 1 < b 1 < a 2 < b 2 < … < b n < …, $\mathop {\lim }\limits_{n \to \infty } $ b n = ∞. Let α(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)e?α(t) vanishing at infinity.
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