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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Addendum to: “Arithmetic means of Fourier coefficients” (Proc. Amer. Math. Soc. 55 (1976), no. 1, 83–86)
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by Rajendra Sinha PDF
Proc. Amer. Math. Soc. 60 (1976), 243-244 Request permission

Abstract:

Let f be integrable and periodic with period 2$2\pi$. Then a necessary and sufficient condition for $\tilde f$ to be equivalent to a continuous function is that $- (1/\pi )\smallint _t^\pi (f(x + u) - f(x - u))/2\tan (u/2) du$ converges uniformly in x as $t \to 0 +$.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 243-244
  • MSC: Primary 42A16
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0420109-2
  • MathSciNet review: 0420109