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Convergence of modified complex trigonometric sums in the metric space \(L\). (English) Zbl 1256.42007

Summary: We study the \(L^1\)-convergence of new modified complex trigonometric sums and obtain a new necessary and sufficient condition for the \(L^1\)-convergence of Fourier series.

MSC:

42A20 Convergence and absolute convergence of Fourier and trigonometric series
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References:

[1] J. Kaur and S. S. Bhatia, Convergence Of New Modified Trigonometric Sums In The Metric Space L, J. Nonlinear Anal. Appl. 1, 1 (2008). · Zbl 1158.42301
[2] J. Kaur and S. S. Bhatia, AClass of L 1-convergenece of new modified cosine sum, Southeast Asian Bulletin of Mathematics, (to appear).
[3] K. Kaur, S. S. Bhatia, and B. Ram, L 1-convergence of certain trigonometric sums, GeorgianMath. J. 11(1), 99 (2004). · Zbl 1051.42004
[4] S. S. Bhatia and B. Ram, The extensions of the F. Móricz theorems, Proc. Amer. Math. Soc. 6(124), 1821 (1996). · Zbl 0867.42002 · doi:10.1090/S0002-9939-96-03212-1
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