Abstract
Given a compact interval I⊆R, and a function f that is a product of a polynomial with a Gaussian, it will be shown that the translates {f(⋅−λ):λ∈Λ} are complete in C(I) if and only if the series of reciprocals of Λ diverge. This extends a theorem in [R. A. Zalik, Trans. Amer. Math. Soc. 243, 299-308]. An additional characterization is obtained when Λ is an arithmetic progression, and the generator f constitutes a linear combination of translates of a function with sufficiently fast decay.
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