On L^1-Convergence Of Rees-Stanojević's Sums With Coefficients From The Class K

On L^1-Convergence Of Rees-Stanojević's Sums With Coefficients From The Class K

In this paper are considered the modified cosine sums introduced by Rees and Stanojević&nbsp; with coefficients from the class <strong>K</strong>. In addition, it is proved that the condition $\lim_{n\to \infty}|a_{n+1}|\log n= 0$ is a necessary and sufficient condition for the $L^{1...

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Main Author: Xhevat Z. Krasniqi
Format: Article
Language:English
Published: Università degli Studi di Catania 2010-12-01
Series:Le Matematiche
Subjects:
Cosine sums
Conjugate Fejer kernel
$L^{1}$-convergence.
Online Access:http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/473
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spelling doaj-08acbbb0de9c42a4a15ff2b00b5d33ab2020-11-25T03:32:25ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52982010-12-016522532755On L^1-Convergence Of Rees-Stanojević's Sums With Coefficients From The Class KXhevat Z. Krasniqi0University of PishtinaIn this paper are considered the modified cosine sums introduced by Rees and Stanojević&nbsp; with coefficients from the class <strong>K</strong>. In addition, it is proved that the condition $\lim_{n\to \infty}|a_{n+1}|\log n= 0$ is a necessary and sufficient condition for the $L^{1}$-convergence of the cosine series. Also, an open problem about $L^{1}$-convergence for the $r-th$ derivative&nbsp; of the cosine series is presented.http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/473Cosine sumsConjugate Fejer kernel$L^{1}$-convergence.
collection DOAJ
language English
format Article
sources DOAJ
author Xhevat Z. Krasniqi
spellingShingle Xhevat Z. Krasniqi
On L^1-Convergence Of Rees-Stanojević's Sums With Coefficients From The Class K
Le Matematiche
Cosine sums
Conjugate Fejer kernel
$L^{1}$-convergence.
author_facet Xhevat Z. Krasniqi
author_sort Xhevat Z. Krasniqi
title On L^1-Convergence Of Rees-Stanojević's Sums With Coefficients From The Class K
title_short On L^1-Convergence Of Rees-Stanojević's Sums With Coefficients From The Class K
title_full On L^1-Convergence Of Rees-Stanojević's Sums With Coefficients From The Class K
title_fullStr On L^1-Convergence Of Rees-Stanojević's Sums With Coefficients From The Class K
title_full_unstemmed On L^1-Convergence Of Rees-Stanojević's Sums With Coefficients From The Class K
title_sort on l^1-convergence of rees-stanojević's sums with coefficients from the class k
publisher Università degli Studi di Catania
series Le Matematiche
issn 0373-3505
2037-5298
publishDate 2010-12-01
description In this paper are considered the modified cosine sums introduced by Rees and Stanojević&nbsp; with coefficients from the class <strong>K</strong>. In addition, it is proved that the condition $\lim_{n\to \infty}|a_{n+1}|\log n= 0$ is a necessary and sufficient condition for the $L^{1}$-convergence of the cosine series. Also, an open problem about $L^{1}$-convergence for the $r-th$ derivative&nbsp; of the cosine series is presented.
topic Cosine sums
Conjugate Fejer kernel
$L^{1}$-convergence.
url http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/473
work_keys_str_mv AT xhevatzkrasniqi onl1convergenceofreesstanojevicssumswithcoefficientsfromtheclassk
_version_ 1724568506461061120

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