Characterization of the fourier series of a distribution having a value at a point
Let f be a periodic distribution of period 2π. Let ∑∞n=-∞aneinθ be its Fourier series. We show that the distributional point value f(θ0) exists and equals γ if and only if the partial sums ∑-x≤n≤ax einθ0 converge to γ in the Cesàro sense as x → ∞ for each a > 0. © 1996 American Mathematical Society.
Publication Source (Journal or Book title)
Proceedings of the American Mathematical Society
Estrada, R. (1996). Characterization of the fourier series of a distribution having a value at a point. Proceedings of the American Mathematical Society, 124 (4), 1205-1212. https://doi.org/10.1090/s0002-9939-96-03174-7