Approximation of signals (functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series
Abstract To start with, signals are dealt with as functions of one variable and images are shown by elements of two variables. The investigation of these ideas is directly related to the transpiring area of information technology. The approximation properties of the periodic signals in L r ( r ≥ 1 )...
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Online Access: | http://link.springer.com/article/10.1186/s13660-016-1101-5 |
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doaj-df3085bb5c5349f5a75c7c36bbb791842020-11-24T22:01:46ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-06-012016111010.1186/s13660-016-1101-5Approximation of signals (functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier seriesDeepmala0Laurian-Ioan Piscoran1SQC and OR Unit, Indian Statistical InstituteDepartment of Mathematics and Computer Science, North University Center of Baia Mare, Technical University of Cluj NapocaAbstract To start with, signals are dealt with as functions of one variable and images are shown by elements of two variables. The investigation of these ideas is directly related to the transpiring area of information technology. The approximation properties of the periodic signals in L r ( r ≥ 1 ) $L^{r}\ (r \geq1)$ -spaces, Lipschitz classes Lipα, Lip ( α , r ) $\operatorname{Lip}(\alpha, r)$ , Lip ( ξ ( t ) , r ) $\operatorname{Lip}(\xi(t), r)$ , and a weighted Lipschitz class W ( L r , ξ ( t ) ) $W(L^{r}, \xi( t))$ through a Fourier series, known as the Fourier approximation in the approximation theory, have wide applications in digital filters and signal analysis. The goal of our paper is to concentrate on the approximation properties of the periodic signals (functions) in the Lipschitz classes by almost Riesz means of the Fourier series associated with the function f. We additionally take note of the fact that our outcomes give sharper estimates than the estimates in some of the known results.http://link.springer.com/article/10.1186/s13660-016-1101-5degree of approximationtrigonometric Fourier approximationW ( L r , ξ ( t ) ) $W(L^{r}, \xi( t))$ -class of functionsalmost Riesz means |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Deepmala Laurian-Ioan Piscoran |
spellingShingle |
Deepmala Laurian-Ioan Piscoran Approximation of signals (functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series Journal of Inequalities and Applications degree of approximation trigonometric Fourier approximation W ( L r , ξ ( t ) ) $W(L^{r}, \xi( t))$ -class of functions almost Riesz means |
author_facet |
Deepmala Laurian-Ioan Piscoran |
author_sort |
Deepmala |
title |
Approximation of signals (functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series |
title_short |
Approximation of signals (functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series |
title_full |
Approximation of signals (functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series |
title_fullStr |
Approximation of signals (functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series |
title_full_unstemmed |
Approximation of signals (functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series |
title_sort |
approximation of signals (functions) belonging to certain lipschitz classes by almost riesz means of its fourier series |
publisher |
SpringerOpen |
series |
Journal of Inequalities and Applications |
issn |
1029-242X |
publishDate |
2016-06-01 |
description |
Abstract To start with, signals are dealt with as functions of one variable and images are shown by elements of two variables. The investigation of these ideas is directly related to the transpiring area of information technology. The approximation properties of the periodic signals in L r ( r ≥ 1 ) $L^{r}\ (r \geq1)$ -spaces, Lipschitz classes Lipα, Lip ( α , r ) $\operatorname{Lip}(\alpha, r)$ , Lip ( ξ ( t ) , r ) $\operatorname{Lip}(\xi(t), r)$ , and a weighted Lipschitz class W ( L r , ξ ( t ) ) $W(L^{r}, \xi( t))$ through a Fourier series, known as the Fourier approximation in the approximation theory, have wide applications in digital filters and signal analysis. The goal of our paper is to concentrate on the approximation properties of the periodic signals (functions) in the Lipschitz classes by almost Riesz means of the Fourier series associated with the function f. We additionally take note of the fact that our outcomes give sharper estimates than the estimates in some of the known results. |
topic |
degree of approximation trigonometric Fourier approximation W ( L r , ξ ( t ) ) $W(L^{r}, \xi( t))$ -class of functions almost Riesz means |
url |
http://link.springer.com/article/10.1186/s13660-016-1101-5 |
work_keys_str_mv |
AT deepmala approximationofsignalsfunctionsbelongingtocertainlipschitzclassesbyalmostrieszmeansofitsfourierseries AT laurianioanpiscoran approximationofsignalsfunctionsbelongingtocertainlipschitzclassesbyalmostrieszmeansofitsfourierseries |
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