Journal article
Finite dimensional H-invariant spaces
Bulletin of the Australian Mathematical Society, Vol.56(03), pp.353-361
1997
Abstract
A subset V of M(G) is left H-invariant if it is invariant under left translation by the elements of H, a subset of a locally compact group G. We establish necessary and sufficient conditions on H which ensure that finite dimensional subspaces of M(G) when G is compact, or of L∞(G) when G is locally compact Abelian, which are invariant in this weaker sense, contain only trigonometric polynomials. This generalises known results for finite dimensional G-invariant subspaces. We show that if H is a subgroup of finite index in a compact group G, and the span of the H-translates of μ is a weak*-closed subspace of L∞(G) or M(G) (or is closed in Lp(G)for 1 ≤ p < ∞), then μ is a trigonometric polynomial.
We also obtain some results concerning functions that possess the analogous weaker almost periodic condition relative to H.
Details
- Title
- Finite dimensional H-invariant spaces
- Authors/Creators
- K.E. Hare (Author/Creator)J.A. Ward (Author/Creator)
- Publication Details
- Bulletin of the Australian Mathematical Society, Vol.56(03), pp.353-361
- Publisher
- Cambridge University Press
- Identifiers
- 991005542382707891
- Copyright
- © Australian Mathematical Society 1997
- Murdoch Affiliation
- School of Mathematical and Physical Sciences
- Language
- English
- Resource Type
- Journal article
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