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