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Absolutely convergent Fourier series of distributions


Author: Nicolas K. Artémiadis
Journal: Proc. Amer. Math. Soc. 83 (1981), 276-278
MSC: Primary 42A20; Secondary 46F10
DOI: https://doi.org/10.1090/S0002-9939-1981-0624913-9
MathSciNet review: 624913
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Abstract: Let $ S$ be a distribution (in the sense of L. Schwartz) defined on the circle $ T$, and suppose that $ S$ is equal to a function in $ {L^\infty }$ on an open interval of $ T$. A necessary and sufficient condition is given in order that the Fourier series of $ S$ converges absolutely.


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

  • [1] N. Artémiadis, Criteria for absolute convergence of Fourier series, Proc. Amer. Math. Soc. 50 (1975), 179-183. MR 0377398 (51:13570)
  • [2] -, Criteria for absolute convergence of Fourier series, Proc. Conf. Harmonic Analysis, Lecture Notes in Math., vol. 781, Springer-Verlag, Berlin and New York, 1978, pp. 1-7. MR 571492 (81d:42012)
  • [3] R. E. Edwards, Fourier series, vol. II, Holt, Rinehart and Winston, New York, 1967.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0624913-9
Article copyright: © Copyright 1981 American Mathematical Society

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