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Lobachevskii Journal of Mathematics, 2003, Volume 13, Pages 39–44 (Mi ljm96)  
Tauberian conditions for $L^1$-convergence of modified complex trigonometric sums

K. Kaur

Govt. Polytechnic Institute
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Abstract: An $L^1$-convergence property of the complex form $g_n(c,t)=S_n(c,t)-[c_nE_n(t)+c_{-n}E_{-n}(t)]$ of the modified sums introduced by Garrett and Stanojević [3] is established and a necessary and sufficient condition for $L^1$-convergence of Fourier series is obtained.
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Language: English
Citation: K. Kaur, “Tauberian conditions for $L^1$-convergence of modified complex trigonometric sums”, Lobachevskii J. Math., 13 (2003), 39–44
Citation in format AMSBIB
\Bibitem{Kau03}
\by K.~Kaur
\paper Tauberian conditions for $L^1$-convergence of modified complex trigonometric sums
\jour Lobachevskii J. Math.
\yr 2003
\vol 13
\pages 39--44
\mathnet{http://mi.mathnet.ru/ljm96}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2025557}
\zmath{https://zbmath.org/?q=an:1044.42004}
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