polynomial trend

The necessary and sufficient conditions are obtained for the lacunary polynomials to be dense in C_α,where C_α is the weighted Banach space of complex continuous functions f(t) on R with f(t)exp｛-α(t)｝ vanishing at infinity.

设函数α(t)在R上非负连续,Cα是R上满足lim|t|→∞f(t)e-α(t)=0的连续函数f(t)全体组成的Banach空间,得到了一个缺项多项式在Cα空间中稠密的充分必要条件。