Let φ be an admissible wavelet for an irreducible and square-integrable representation π: G → U(X) of a locally compact and Hausdorff group G on a Hilbert space X. In this chapter we introduce a class of bounded linear operators L F,φ : X → X, which are related to the wavelet transform A φ : X → L 2 (G) defined by (7.1), for all F in L P (G),1 ≤ p ≤ ∞. We first tackle this problem for F in L1(G) or L ∞(G). In the case when p = 1, we do not need the assumption that the representation π : G → U(X) be irreducible.
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