Note on a Result of Kerman and Weit II |
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Authors: | Swagato K Ray Rudra P Sarkar |
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Institution: | 1. Stat-Math Unit, Indian Statistical Institute, 203 B.T. Rd., Calcutta, 700108, India
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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 {f n ∣n=1,2,3,…} is dense in L p (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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