A note on approximation by automorphic images of functions in L1 and L∞

Abstract

In [1], it was shown that if ƒ ∈ Lp(Rn), where 1 < p < ∞, then the closed subspace of Lp (Rn) spanned by functions of the form [where a1, …, an, b1, …, bn, are real numbers; ak, ≠ 0; k = 1, …, n] coincides with the whole of Lp(Rn). In the present note, analogous results are derived for the spaces of integrable functions, essentially bounded measurable functions, bounded continuous functions, and continuous functions vanishing at infinity.