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A non-MRA $C^r$ frame wavelet with rapid decay

Lawrence Baggett·Palle Jorgensen·Kathy Merrill·Judith Packer
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Abstract

A generalized filter construction is used to build an example of a non-MRA normalized tight frame wavelet for dilation by 2 in $L^2(\mathbb R)$. 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 positive integer $r$.

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Lawrence Baggett, Palle Jorgensen, Kathy Merrill, Judith Packer. 2005-12-02. A non-MRA $C^r$ frame wavelet with rapid decay. https://arxiv.org/abs/math/0504394

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