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Some compactly supported dual wavelets associated to the Quincunx matrix in $ℝ^{3}$

M. L. Arenas-Blázquez

Departamento de Matemáticas, Universidad de Alicante, 03080 Alicante, Spain

E-mail Address: mluisab.arenas@gmail.com

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and

A. San Antolín

https://orcid.org/0000-0002-3584-9667

Departamento de Matemáticas, Universidad de Alicante, 03080 Alicante, Spain

E-mail Address: angel.sanantolin@ua.es

Corresponding author.

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https://doi.org/10.1142/S0219691324500218Cited by:0 (Source: Crossref)

Abstract

In this paper, we construct a family of compactly supported dual wavelets associated to the Quincunx matrix on $ℝ^{3}$ . Our family will have dual wavelets with any desired number of vanishing moments, any fixed degree of regularity and symmetry with respect to some point. Finally, we also present dual wavelets on $L^{2} (ℝ^{2})$ associated to some dilation matrices with determinant $2$ .

Keywords:

AMSC: 42C40

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