Fundamental sets of functions on locally compact abelian groups. (English) Zbl 1332.43003
Let \(G\) be a locally compact abelian group and let \(X\) be a compact subset of \(X\). For a function \(\varphi:G\to{\mathbb C}\), the author studies the question of when the set \(\{x\mapsto\varphi(x-y):y\in X\}\) is dense in the space of continuous functions on \(X\).
Reviewer: Vladimir V. Peller (East Lansing)
MSC:
| 43A22 | Homomorphisms and multipliers of function spaces on groups, semigroups, etc. |
| 41A30 | Approximation by other special function classes |
| 42C30 | Completeness of sets of functions in nontrigonometric harmonic analysis |
| 43A70 | Analysis on specific locally compact and other abelian groups |
| 41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |
| 43A40 | Character groups and dual objects |
Keywords:
Bochner’s theorem; character group; dual group; equicontinuity; locally compact abelian group; \(\sigma\)-compact group; topological groupReferences:
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