Wavelet packet approximation theorem for Hr type norm. Issue 3 (4th March 2019)

• Record Type: Journal Article
• Authors: Khanna, Nikhil; Kaushik, S. K.
• Is Part Of: Integral transforms and special functions. Volume 30:Issue 3(2019)
• Page Start: 231
• Page End: 239
• Publication Date: 2019-03-04
• Subjects: MRA -- wavelet packets -- Coifman wavelet packet system -- moments; 42C40 -- 44A60 -- 65T60; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2018.1555585
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: In this paper, we give the wavelet packet approximation theorem forH r type norm which can measure difference of the (weak) derivatives. We will show that with equal distribution of the vanishing moments between the scaling functionω 0 and the wavelet packetsω n, n ∈ N, if the sample values of a smooth function as scaling function coefficients at a fine scale are used, then the wavelet packet series approximates the smooth function under consideration with increasing verity inH r type norm as the number of vanishing moments M increases or the scale J gets finer.