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 $t \to 0 +$.References
- Rajendra Sinha, Arithmetic means of Fourier coefficients, Proc. Amer. Math. Soc. 55 (1976), no. 1, 83–86. MR 397274, DOI 10.1090/S0002-9939-1976-0397274-9
- Marc Zamansky, Sur l’approximation des fonctions continues périodiques, C. R. Acad. Sci. Paris 228 (1949), 460–461 (French). MR 28450
- A. Zygmund, Trigonometric series: Vols. I, II, Cambridge University Press, London-New York, 1968. Second edition, reprinted with corrections and some additions. MR 0236587
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