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

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

2005-04-19

arxiv.org/abs/math/0504394v3

Acta Appl. Math. 89 (2006), 251--270

Mathematics

Classical Analysis and ODEs

20 pages; v2 has graphics for Figures 1, 2, 3, 4; v3 has Figures 5, 6; accepted in 'Acta Applicandae Mathematicae'

Scientific paper

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 Journ\'e 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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