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2013 Some Bivariate Smooth Compactly Supported Tight Framelets with Three Generators
A. San Antolín, R. A. Zalik
Abstr. Appl. Anal. 2013: 1-7 (2013). DOI: 10.1155/2013/818907


For any 2 × 2 dilation matrix with integer entries and | det  A | = 2 , we construct a family of smooth compactly supported tight wavelet frames with three generators in L 2 ( 2 ) . Our construction involves some compactly supported refinable functions, the oblique extension principle, and a slight generalization of a theorem of Lai and Stöckler. Estimates for the degrees of smoothness are given. With the exception of a polynomial whose coefficients must in general be computed by spectral factorization, the framelets are expressed in closed form in the frequency domain, in terms of elementary transcendental functions. By means of two examples we also show that for low degrees of smoothness the use of spectral factorization may be avoided.


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A. San Antolín. R. A. Zalik. "Some Bivariate Smooth Compactly Supported Tight Framelets with Three Generators." Abstr. Appl. Anal. 2013 1 - 7, 2013.


Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1276.42026
MathSciNet: MR3055947
Digital Object Identifier: 10.1155/2013/818907

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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