Absolutely convergent Fourier series of distributions
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- by Nicolas K. Artémiadis
- Proc. Amer. Math. Soc. 83 (1981), 276-278
- DOI: https://doi.org/10.1090/S0002-9939-1981-0624913-9
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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
- Nicolas Artémiadis, Criteria for absolute convergence of Fourier series, Proc. Amer. Math. Soc. 50 (1975), 179–183. MR 377398, DOI 10.1090/S0002-9939-1975-0377398-1
- Nicolas K. Artémiades, Criteria for absolute convergence of Fourier series, Harmonic analysis, Iraklion 1978 (Proc. Conf., Univ. Crete, Iraklion, 1978), Lecture Notes in Math., vol. 781, Springer, Berlin, 1980, pp. 1–7. MR 571492 R. E. Edwards, Fourier series, vol. II, Holt, Rinehart and Winston, New York, 1967.
Bibliographic Information
- © Copyright 1981 American Mathematical Society
- 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