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A generalized filter construction is used to build an example of a non-MRA normalized tight frame wavelet for dilation by 2 in $$L^{2} {\left( \mathbb{R} \right)}$$ . This example has the same multiplicity function as the Journé wavelet, yet has a $$C^{\infty } $$ Fourier transform and can be made to be $$C^{r} $$ for any fixed postive integer $$r$$ .
Acta Applicandae Mathematicae – Springer Journals
Published: Mar 4, 2006
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