Images of the continuous wavelet transform (original) (raw)

Keith Taylor

2014, Contemporary Mathematics

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10 pages

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A wavelet, in the generalized sense, is a vector in the Hilbert space, Hπ, of a unitary representation, π, of a locally compact group, G, with the property that the wavelet transform it defines is an isometry of Hπ into L 2 (G). We study the image of this transform and how that image varies as the wavelet varies. We obtain a version of the Peter-Weyl Theorem for the class of groups for which the regular representation is a direct sum of irreducible representations.