## Archival Version

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://www.math.psu.edu/era/.
**

Wavelets on general lattices,
associated with general expanding maps of $\mathbf R^n$
**This journal is archived by the American Mathematical
Society. The master copy is available at
http://www.ams.org/era/
**

## 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*

**Retrieve entire article **

#### 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`

*Electronic Research Announcements of the AMS *Home page