Generalized Shift Invariant Subspaces; Special Representations of Abelian Groups
||Prof. Edward N. Wilson, Washington University in St. Louis, Missouri, USA
||Generalized Shift Invariant Subspaces; Special Representations of Abelian Groups
We will consider unitary representations of a locally
compact abelian group G for which every cyclic subrepresentation is
equivalent to a subrepresentation of the regular representation of G, i.e. the representation acting by translation on L^2(G) relative to any Haar measure on G. We will give a characterization of these representations in terms of an integrability property and use this property to unify the treatment of cyclic (or principal shift invariant) subspaces of L^2(R^n) arising from translation, modulation, and dilation representations of abelian groups isomorphic to finite products of the integers.
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