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Mollification Based on Wavelets

Tohoku University, Sendai 980-8577, Japan
College of Engineering, Nihon University, Koriyama 963-8642, Japan
Author to whom correspondence should be addressed.
Axioms 2013, 2(2), 67-84;
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)
PDF [626 KB, uploaded 25 March 2013]


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. View Full-Text
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

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

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