Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation

A sufficient literature is available for the wavelet error of approximation of certain functions in the L2-norm. There is no work in context of multiresolution approximation of a function in the sense of sup-error. In this paper, for the first time, wavelet estimator for the approximation of a funct...

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Main Authors: Shyam Lal, Susheel Kumar
Format: Article
Language:English
Published: Wiley 2016-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2016/9121249
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author Shyam Lal
Susheel Kumar
author_facet Shyam Lal
Susheel Kumar
author_sort Shyam Lal
collection DOAJ
description A sufficient literature is available for the wavelet error of approximation of certain functions in the L2-norm. There is no work in context of multiresolution approximation of a function in the sense of sup-error. In this paper, for the first time, wavelet estimator for the approximation of a function f belonging to Lipα[a,b] class under supremum norm has been obtained. Working in this direction, four new theorems on the wavelet approximation of a function f belonging to Lipα,0<α≤1 class using the projection Pmf of its wavelet expansions have been estimated. The calculated estimator is best possible in wavelet analysis.
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spelling doaj-art-cd7ece7b3bd5498ca05d242b3f31f1ca2025-08-20T02:19:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252016-01-01201610.1155/2016/91212499121249Quasi-Positive Delta Sequences and Their Applications in Wavelet ApproximationShyam Lal0Susheel Kumar1Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, IndiaDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, IndiaA sufficient literature is available for the wavelet error of approximation of certain functions in the L2-norm. There is no work in context of multiresolution approximation of a function in the sense of sup-error. In this paper, for the first time, wavelet estimator for the approximation of a function f belonging to Lipα[a,b] class under supremum norm has been obtained. Working in this direction, four new theorems on the wavelet approximation of a function f belonging to Lipα,0<α≤1 class using the projection Pmf of its wavelet expansions have been estimated. The calculated estimator is best possible in wavelet analysis.http://dx.doi.org/10.1155/2016/9121249
spellingShingle Shyam Lal
Susheel Kumar
Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation
International Journal of Mathematics and Mathematical Sciences
title Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation
title_full Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation
title_fullStr Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation
title_full_unstemmed Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation
title_short Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation
title_sort quasi positive delta sequences and their applications in wavelet approximation
url http://dx.doi.org/10.1155/2016/9121249
work_keys_str_mv AT shyamlal quasipositivedeltasequencesandtheirapplicationsinwaveletapproximation
AT susheelkumar quasipositivedeltasequencesandtheirapplicationsinwaveletapproximation