The left regular representation L: G→U(L 2 (G)) of a locally compact and Hausdorff group G given by (L(g)u)(h) = u(g -1 h), g, h∈G, for all u in L 2 (G), has been playing a subsidiary role since its appearance in Example 5.7. In this chapter we show that it is an object of interest in its own right. We are particularly interested in the adjoints of wavelet transforms for left regular representations of unimodular groups.
KeywordsBounded Linear Operator Convolution Operator Modular Group Regular Representation Left Translation
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