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Characterization of the Fourier series
of a distribution having a value at a point


Author: Ricardo Estrada
Journal: Proc. Amer. Math. Soc. 124 (1996), 1205-1212
MSC (1991): Primary 46F10, 42A24
DOI: https://doi.org/10.1090/S0002-9939-96-03174-7
MathSciNet review: 1307515
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Abstract: Let $f$ be a periodic distribution of period $2\pi$. Let $\sum^\infty_{n=-\infty} a_ne^{in\theta}$ be its Fourier series. We show that the distributional point value $f(\theta_0)$ exists and equals $\gamma$ if and only if the partial sums $\sum_{-x\le n\le ax}a_ne^{in\theta_0}$ converge to $ \gamma$ in the Cesàro sense as $x\to \infty$ for each $a>0$.


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Additional Information

Ricardo Estrada
Affiliation: Department of Mathematics, Texas A & M University, College Station, Texas 77843
Address at time of publication: P. O. Box 276, Tres Ríos, Costa Rica
Email: restrada@cariari.ucr.ac.cr

DOI: https://doi.org/10.1090/S0002-9939-96-03174-7
Received by editor(s): May 2, 1994
Received by editor(s) in revised form: October 18, 1994
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society

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