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# Absolutely Convergent Fourier Series of Distributions

Proceedings of the American Mathematical Society
Vol. 83, No. 2 (Oct., 1981), pp. 276-278
DOI: 10.2307/2043510
Stable URL: http://www.jstor.org/stable/2043510
Page Count: 3
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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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