Images of the continuous wavelet transform
Mahya Ghandehari, Keith Taylor · Contemporary mathematics - American Mathematical Society · 2014
A wavelet, in the generalized sense, is a vector in the Hilbert space, H π {\mathcal H}_\pi , of a unitary representation, π \pi , of a locally compact group, G G , with the property that the wavelet transform it defines is an isometry of H π {\mathcal H}_\pi into L 2 ( G ) 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.