Approximation by group invariant subspaces
- Barbieri, Davide
- Cabrelli, Carlos
- Hernández, Eugenio
- Molter, Ursula Maria
DOIAbstract
In this article we study the structure of Γ-invariant spaces of L2(S). Here S is a second countable LCA group. The invariance is with respect to the action of Γ, a non commutative group in the form of a semidirect product of a discrete cocompact subgroup of S and a group of automorphisms. This class includes in particular most of the crystallographic groups. We obtain a complete characterization of Γ-invariant subspaces in terms of range functions associated to shift-invariant spaces. We also define a new notion of range function adapted to the Γ-invariance and construct Parseval frames of orbits of some elements in the subspace, under the group action. These results are then applied to prove the existence and construction of a Γ-invariant ...
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