The linear operator A ϕ : X → G 2(G) used in the proof of the resolution of the identity formula (6.3) in the previous chapter plays a pivotal role in this book. It is in fact the wavelet transform associated to the admissible wavelet yo for the irreducible and square-integrable representation π: G → U(X) of a locally compact and Hausdorff group G on a Hilbert space. To be more precise, we introduce the following definition.
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