A family of nonseparable scaling functions and compactly supported tight framelets

Given integers b and d, with d>1 and |b|>1, we construct even nonseparable compactly supported refinable functions with dilation factor b that generate multiresolution analyses on L2(Rd). These refinable functions are nonseparable, in the sense that they cannot be expressed as the product of t...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 404; no. 2; pp. 201 - 211
Main Authors San Antolín, A., Zalik, R.A.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.08.2013
Subjects
Fourier transform
Low pass filter
Multiresolution analysis
Paley–Wiener theorem for several complex variables
Riesz basis
Scaling function
Tight framelet
Scaling function
Paley–Wiener theorem for several complex variables
Fourier transform
Low pass filter
Multiresolution analysis
Riesz basis
Tight framelet
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Summary:Given integers b and d, with d>1 and |b|>1, we construct even nonseparable compactly supported refinable functions with dilation factor b 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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2013.02.040