Mollification Based on Wavelets

Axioms

Tohru Morita¹ 

[1] Tohoku University, Sendai 980-8577, Japan; E-Mail:

关键词: mollification;    Gibbs phenomenon;    rapidly decaying harmonic wavelet;    B-spline;    Lanczos’ σ-factor;   

DOI  :  10.3390/axioms2020067

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.