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Axioms 2013, 2(2), 67-84; doi:10.3390/axioms2020067

Mollification Based on Wavelets

1 Tohoku University, Sendai 980-8577, Japan 2 College of Engineering, Nihon University, Koriyama 963-8642, Japan
* Author to whom correspondence should be addressed.
Received: 9 January 2013 / Revised: 11 March 2013 / Accepted: 19 March 2013 / Published: 25 March 2013
(This article belongs to the Special Issue Wavelets and Applications)
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The mollification obtained by truncating the expansion in wavelets is studied, where the wavelets are so chosen that noise is reduced and the Gibbs phenomenon does not occur. The estimations of the error of approximation of the mollification are given for the case when the fractional derivative of a function is calculated. Noting that the estimations are applicable even when the orthogonality of the wavelets is not satisfied, we study mollifications using unorthogonalized wavelets, as well as those using orthogonal wavelets.
Keywords: mollification; Gibbs phenomenon; rapidly decaying harmonic wavelet; B-spline; Lanczos’ σ-factor mollification; Gibbs phenomenon; rapidly decaying harmonic wavelet; B-spline; Lanczos’ σ-factor
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Morita, T.; Sato, K.-I. Mollification Based on Wavelets. Axioms 2013, 2, 67-84.

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