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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Absolutely convergent Fourier series of distributions


Author: Nicolas K. Artémiadis
Journal: Proc. Amer. Math. Soc. 83 (1981), 276-278
MSC: Primary 42A20; Secondary 46F10
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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0624913-9
PII: S 0002-9939(1981)0624913-9
Article copyright: © Copyright 1981 American Mathematical Society