Abstract:We investigate the wavelet spaces Wg(Hπ) ⊂ L 2 (G) arising from square integrable representations π : G → U(Hπ) of a locally compact group G. We show that the wavelet spaces are rigid in the sense that non-trivial intersection between them imposes strong restrictions. Moreover, we use this to derive consequences for wavelet transforms related to convexity and functions of positive type. Motivated by the reproducing kernel Hilbert space structure of wavelet spaces we examine an interpolation problem. In the set… Show more
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