Proves that sparse, almost-integer, and two-difference sequences of translates span L^p(R) for 1<p≤2, with constructions shown to be sharp against known lacunary and arithmetic-progression obstructions.
Olevskii, Approximation by translates in L^2( ) , Real Anal
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Completeness of sparse, almost integer and finite local complexity sequences of translates in $L^p(\mathbb{R})$
Proves that sparse, almost-integer, and two-difference sequences of translates span L^p(R) for 1<p≤2, with constructions shown to be sharp against known lacunary and arithmetic-progression obstructions.