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Characterization of the Fourier series of a distribution having a value at a point
Authors:Ricardo Estrada
Affiliation:Department of Mathematics, Texas A & M University, College Station, Texas 77843
Abstract:Let $f$ be a periodic distribution of period $2pi$. Let $sum^infty_{n=-infty} a_ne^{intheta}$ 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 $sum_{-xle nle ax}a_ne^{intheta_0}$ converge to $ gamma$ in the Cesàro sense as $xto infty$ for each $a>0$.

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