Abstract
Let G be a locally compact topological group, equipped with a fixed left Haar measure μ. We show that if f is a compactly supported real valued continuous function on G which has a unique maximum or a unique minimum at a point in G, then the space generated by the span of left translations of {fn∣n=1,2,3,…} is dense in Lp(G,μ), 1≤p<∞, in the space of continuous functions, continuous compactly supported functions and in the space of continuous functions vanishing at ∞. Similar results are true when the group G is substituted by G-spaces with compact isotropy group.
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