On the Continuous Wavelet Transform on Homogeneous Spaces

Let G be a locally compact group with a compact subgroup H. We define a square integrable representation of a homogeneous space G/H on a Hilbert space . 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 that the range of the continuous wavelet transform is a reproducing kernel Hilbert space. Moreover, we obtain a necessary and sufficient condition for the continuous wavelet transform to be onto.

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