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

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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 $L^2(\mathbb R)$. 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 $r$.
20 pages; v2 has graphics for Figures 1, 2, 3, 4; v3 has Figures 5, 6; accepted in 'Acta Applicandae Mathematicae'

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Classical Analysis and ODEs, Operator Algebras, 54C40, 14E20 (Primary), 46E25, 20C20 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/101218

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0504394
 http://arxiv.org/abs/math/0504394
 Acta Appl. Math. 89 (2006), 251--270

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arXiv