San Antolín Gil, Ángel, Zalik, Richard A.
Two families of compactly supported Parseval framelets in L2(Rd)
Applied and Computational Harmonic Analysis. 2022, 60: 512-527. https://doi.org/10.1016/j.acha.2022.04.005
URI: http://hdl.handle.net/10045/123714
DOI: 10.1016/j.acha.2022.04.005
ISSN: 1063-5203 (Print)
Abstract: 
For any dilation matrix with integral entries A ∈ Rd×d, d ≥ 1, we construct two families of Parseval wavelet frames in L2(Rd). Both families have compact support and any desired number of vanishing moments. The first family has | detA| generators. The second family has any desired degree of regularity. For the members of this family, the number of generators depends on the dilation matrix A and the dimension d, but never exceeds | detA| + d. Our construction involves trigonometric polynomials developed by Heller to obtain refinable functions, the Oblique Extension Principle, and a slight generalization of a theorem of Lai and Stöckler.
Keywords:Dilation matrix, Fourier transform, Refinable function, Tight framelet, Unitary Extension Principle
Elsevier
info:eu-repo/semantics/article