A family of nonseparable scaling functions and compactly supported tight framelets

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Title: A family of nonseparable scaling functions and compactly supported tight framelets
Authors: San Antolín Gil, Ángel | Zalik, Richard A.
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Análisis Matemático
Keywords: Fourier transform | Multiresolution analysis | Riesz basis | Scaling function | Low pass filter | Tight framelet | Paley–Wiener theorem for several complex variables
Knowledge Area: Análisis Matemático
Issue Date: 15-Aug-2013
Publisher: Elsevier
Citation: Journal of Mathematical Analysis and Applications. 2013, 404(2): 201-211. doi:10.1016/j.jmaa.2013.02.040
Abstract: Given integers b and d, with d>1 and |b|>1, we construct even nonseparable compactly supported refinable functions with dilation factor bb that generate multiresolution analyses on L2(Rd). These refinable functions are nonseparable, in the sense that they cannot be expressed as the product of two functions defined on lower dimensions. We use these scaling functions and a slight generalization of a theorem of Lai and Stöckler to construct smooth compactly supported tight framelets. Both the refinable functions and the framelets they generate can be made as smooth as desired. Estimates for the supports of these refinable functions and framelets, are given.
Sponsor: The first author was partially supported by Spanish Science Ministry grant JC2010-0012.
URI: http://hdl.handle.net/10045/43965
ISSN: 0022-247X (Print) | 1096-0813 (Online)
DOI: 10.1016/j.jmaa.2013.02.040
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
Publisher version: http://dx.doi.org/10.1016/j.jmaa.2013.02.040
Appears in Collections:INV - CADAGL - Artículos de Revistas

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