Wavelets on general lattices, associated with general expanding maps of 𝐑ⁿ

Abstract

In the context of a general lattice Γ \Gamma in R n \mathbf {R}^n and a strictly expanding map M 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 ≥ 1 , d\ge 1, and all the scaling functions. Moreover, we give several examples: in particular, we construct a single, MRA and C ∞ ( R n ) C^\infty (\mathbf {R}^n) wavelet, which is nonseparable and with compactly supported Fourier transform.