Article overview
Abstract
In this paper, linear wavelet approximation of a functions $f$ belonging to Lip$\xi,$ and $Lip(\xi,p), 1 \leq p < \infty,$ have been determined by using Haar scaling function and Haar wavelet series. A non-linear wavelet approximation of function belonging $L^2(\mathbb{R})$ and Lip$\alpha$ class has been obtained. The comparison of the order of linear and non-linear approximations have been studied. It is observed that a non-linear approximation error is better and sharper than linear approximation error.
Keywords and Phrases
Lip$\alpha$ class of functionsLip$(\alphap)$ class of functionsLip$\xi$ class of functionsLip$(\xip)$ class of functionsMultiresolution analysisScaling function $\phi$Linear approximationNon-linear approximation.
AMS Subject Classification
40A30, 42C15, 42A16, 42C40, 65T60, 65L10, 65L60, 65R20.
Reference information
How to Cite
Susheel Kumar (2023). LINEAR AND NON-LINEAR WAVELET APPROXIMATIONS OF FUNCTIONS OF LIPSCHITZ CLASS AND RELATED CLASSES USING THE HAAR WAVELET SERIES. Journal of Ramanujan Society of Mathematics and Mathematical Sciences, 10(2), 161-176.