Density of translates in weighted \(L^{p}\) spaces on locally compact groups. (English) Zbl 1420.47003
Let \(G\) be a locally compact group and let \(1\leq p < \infty\). For a subset \(S\subseteq G\), the authors give a characterization for existence of a vector \(f\) in the weighted \(L^p\)-space \(L^p ( G, \omega ) = \{ h: \int | h \omega |^p < \infty \}\) such that the set of all left translations of the vector \(f\) is dense in \(L^p ( G, \omega )\).
Reviewer: Tianxuan Miao (Thunder Bay)
MSC:
| 47A16 | Cyclic vectors, hypercyclic and chaotic operators |
| 43A15 | \(L^p\)-spaces and other function spaces on groups, semigroups, etc. |
| 37C85 | Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) |
Citations:
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