Existence of multiwavelets in $\mathbb {R}^n$
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- by Carlos A. Cabrelli and María Luisa Gordillo PDF
- Proc. Amer. Math. Soc. 130 (2002), 1413-1424 Request permission
Abstract:
For a $q$-regular Multiresolution Analysis of multiplicity $r$ with arbitrary dilation matrix $A$ for a general lattice $\Gamma$ in $\mathbb {R}^n$, 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 $2r(m-1) \geq n$ where $m$ is the absolute value of the determinant of $A$, then these conditions are always met, and therefore an associated wavelet basis of $q$-regular functions always exists. This extends known results to the case of multiwavelets in several variables with an arbitrary dilation matrix $A$ for a lattice $\Gamma$.References
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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
- MR Author ID: 308374
- ORCID: 0000-0002-6473-2636
- 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
- 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
- © Copyright 2001 American Mathematical Society
- 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
- MathSciNet review: 1879965