Some Smooth Compactly Supported Tight Framelets

A. San Antolín, R. A. Zalik


For any dilation matrix with integer entries, we construct a family of smooth compactly supported tight wavelet frames in $L^2(\mathbb{R}^d)$, $d\ge 1$. Estimates for the degrees of smoothness of these framelets are given. Our construction involves some compactly supported refinable functions, the Oblique Extension Principle and a slight generalization of a theorem of Lai and Stöckler.


Dilation matrix; Fourier transform; Refinable function; Tight framelet

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