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Continuous wavelet transforms on the space \(L^{2}(\mathbf R,\mathbb H; dx)\). (English) Zbl 1040.42031
Summary: Let \(\mathbf P\) be the affine group of the real line \(\mathbf R\), and let \(\mathbb H\) be the set of all quaternions. Thus, \(L^2 (\mathbf R, \mathbb H; dx)\) denotes the space of all square integrable \(\mathbb H\)-valued functions. From the viewpoint of square integrable group representations, we study the theory of continuous wavelet transforms on \(L^2(\mathbf R,\mathbb H; dx)\) associated with the group \(\mathbf P\), and give the Calderón reproducing formula.

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
43A80 Analysis on other specific Lie groups
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