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Wavelets on general lattices, associated with general expanding maps of \(\mathbf R^n\). (English) Zbl 0914.42026
Summary: In the context of a general lattice \(\Gamma\) in \({\mathbb{R}}^n\) and a strictly expanding map \(M\) which preserves the lattice, we characterize all the wavelet families, all the MSF wavelets, all the multiwavelets associated with a Multiresolution Analysis (MRA) of multiplicity \(d\geq 1,\) and all the scaling functions. Moreover, we give several examples: in particular, we construct a single MRA and \(C^\infty({\mathbb{R}}^n)\) wavelet, which is nonseparable and with compactly supported Fourier transform.

MSC:
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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