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In the context of a general lattice $\Gamma$ in $\Rn$ 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 $d\ge1,$ and all the scaling functions. Moreover, we give several examples: in particular, we construct a single, MRA and $C^\infty (\Rn)$ wavelet, which is nonseparable and with compactly supported Fourier transform.

Copyright 1999 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 05 (1999), pp. 1-10
• Publisher Identifier: S 1079-6762(99)00054-2
• 1991 Mathematics Subject Classification. Primary 42C15
• Key words and phrases. Wavelets, multiresolution analysis (MRA), general lattices in ${\mathbf R}^n,$ MSF wavelets, multiwavelets
• Received by the editors July 13, 1998
• Posted on January 25, 1999
• Communicated by Stuart Antman
• Comments (When Available)

A. Calogero

Dipartimento di Matematica, Universit\'a di Milano, via Saldini 50, 20133 Milano, Italy

E-mail address: Calogero@vmimat.mat.unimi.it