【摘 要】
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A necessary and sufficient condition is obtained for the incompleteness of a complex exponential system E(A, M) in Cα, where Cα is the weighted Banach space c
【机 构】
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School of Mathematical Sciences
论文部分内容阅读
A necessary and sufficient condition is obtained for the incompleteness of a complex exponential system E(A, M) in Cα, where Cα is the weighted Banach space consisting of all complex continuous functions f on the real axis R with f(t)exp(-α(t)) vanishing at infinity, in the uniform norm ‖f‖α = sup{|f(t)e-α(t)|: t ∈ R} with respect to the weight α(t). If the incompleteness holds, then the complex exponential system E(∧, M) is minimal and each function in the closure of the linear span of complex exponential system E(∧, M) can be extended to an entire function represented by a Taylor-Dirichlet series.
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