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This paper develops several aspects of shift-invariant spaces on locally compact abelian groups. For a second countable locally compact abelian group G we prove a useful Hilbert space isomorphism, introduce range functions and give a characterization of shift-invariant subspaces of L 2 (G) in terms of range functions. Utilizing these functions, we… (More)

Let G be a locally compact group with a compact subgroup H. We define a square inte-grable representation of a homogeneous space G/H on a Hilbert space H. The reconstruction formula for G/H is established and as a result it is concluded that the set of admissible vectors is path connected. The continuous wavelet transform on G/H is defined and it is shown… (More)

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