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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.
Received: 9 January 2013; in revised form: 11 March 2013 / Accepted: 19 March 2013 / Published: 25 March 2013
Abstract: 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
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MDPI and ACS Style
Morita, T.; Sato, K.-I. Mollification Based on Wavelets. Axioms 2013, 2, 67-84.
Morita T, Sato K-I. Mollification Based on Wavelets. Axioms. 2013; 2(2):67-84.
Morita, Tohru; Sato, Ken-ichi. 2013. "Mollification Based on Wavelets." Axioms 2, no. 2: 67-84.