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Wavelets on general lattices, associated with general expanding maps of $\mathbf R^n$

Author: A. Calogero
Journal: Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 1-10
MSC (1991): Primary 42C15
Published electronically: January 25, 1999
MathSciNet review: 1667201
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Abstract: In the context of a general lattice $\Gamma$ in $\mathbf {R}^n$ 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 $d\ge 1,$ and all the scaling functions. Moreover, we give several examples: in particular, we construct a single, MRA and $C^\infty (\mathbf {R}^n)$ wavelet, which is nonseparable and with compactly supported Fourier transform.

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Additional Information

A. Calogero
Affiliation: Dipartimento di Matematica, Universitá di Milano, via Saldini 50, 20133 Milano, Italy

Keywords: Wavelets, multiresolution analysis (MRA), general lattices in ${\mathbf R}^n$, $MSF wavelets$, multiwavelets
Received by editor(s): July 13, 1998
Published electronically: January 25, 1999
Communicated by: Stuart Antman
Article copyright: © Copyright 1999 American Mathematical Society