On the Dini test and divergence of Fourier series
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- by Calixto P. Calderón PDF
- Proc. Amer. Math. Soc. 82 (1981), 382-384 Request permission
Abstract:
In this note we prove that no condition weaker than the Dini assures the pointwise convergence of a Fourier series in a set of positive measure.References
- Lennart Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135–157. MR 199631, DOI 10.1007/BF02392815
- Richard A. Hunt, On the convergence of Fourier series, Orthogonal Expansions and their Continuous Analogues (Proc. Conf., Edwardsville, Ill., 1967) Southern Illinois Univ. Press, Carbondale, Ill., 1968, pp. 235–255. MR 0238019 J. Marcinkiewicz, Sur les séries de Fourier, Fund. Math. 27 (1936), 38-69. —, On the convergence of Fourier Series, J. London Math. Soc. 10 (1935), 264-268.
- 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 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 382-384
- MSC: Primary 42A20
- DOI: https://doi.org/10.1090/S0002-9939-1981-0612724-X
- MathSciNet review: 612724