Existence of multiwavelets in

Authors:
Carlos A. Cabrelli and María Luisa Gordillo

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1413-1424

MSC (2000):
Primary 42C40; Secondary 42C30

DOI:
https://doi.org/10.1090/S0002-9939-01-06223-2

Published electronically:
October 12, 2001

MathSciNet review:
1879965

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Abstract: For a -regular Multiresolution Analysis of multiplicity with arbitrary dilation matrix for a general lattice in , we give necessary and sufficient conditions in terms of the mask and the symbol of the vector scaling function in order that an associated wavelet basis exists. We also show that if where is the absolute value of the determinant of , then these conditions are always met, and therefore an associated wavelet basis of -regular functions always exists. This extends known results to the case of multiwavelets in several variables with an arbitrary dilation matrix for a lattice .

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Additional Information

**Carlos A. Cabrelli**

Affiliation:
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428 Capital Federal, Argentina, and CONICET, Argentina

Email:
cabrelli@dm.uba.ar

**María Luisa Gordillo**

Affiliation:
Departamento de Informática, F.C.E.F.y N., Universidad Nacional de San Juan, Avda. José Ignacio de la Roza y Meglioli (5400) San Juan, Argentina

Email:
mluisa@iee.unsj.edu.ar

DOI:
https://doi.org/10.1090/S0002-9939-01-06223-2

Keywords:
Multiresolution Analysis,
dilation matrix,
multiwavelets,
non-separable wavelets,
wavelets

Received by editor(s):
June 23, 2000

Received by editor(s) in revised form:
November 19, 2000

Published electronically:
October 12, 2001

Additional Notes:
The research of the authors is partially supported by grants UBACyT TW84, CONICET, PIP456/98 and BID-1201/OC-AR-PICT-03134

Communicated by:
David R. Larson

Article copyright:
© Copyright 2001
American Mathematical Society