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Proceedings of the American Mathematical Society

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Necessary and sufficient conditions for $ L\sp{1}$ convergence of trigonometric series

Authors: John W. Garrett and Časlav V. Stanojević
Journal: Proc. Amer. Math. Soc. 60 (1976), 68-71
MSC: Primary 42A20
MathSciNet review: 0425480
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Abstract: It is shown that for the class of cosine series satisfying $ a(n)\log n = o(1)$ and $ \Delta a(n) \geqslant 0$ that integrability and $ {L^1}$ convergence occur together. Relaxing the monotonicity to bounded variation we show that our previous result cannot be extended.

References [Enhancements On Off] (What's this?)

  • [1] J. W. Garrett and Č. V. Stanojević, On $ {L^1}$ convergence of certain cosine sums, Proc. Amer. Math. Soc. 54 (1976), 101-105. MR 0394002 (52:14808b)
  • [2] S. A. Teljakovskii, Concerning a sufficient condition of Sidon for the integrability of trigonometric series, Mat. Zametki 14 (1973), 317-328 = Math. Notes 14 (1973), 742-748 (1974). MR 48 #6798. MR 0328456 (48:6798)

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Keywords: $ {L^1}$ convergence of Fourier series, Fejér sums
Article copyright: © Copyright 1976 American Mathematical Society

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