Distributional point values and convergence of fourier series and integrals
Document Type
Article
Publication Date
10-1-2007
Abstract
In this article we show that the distributional point values of a tempered distribution are characterized by their Fourier transforms in the following way: If f ∈S1 (R) and x0 ∈ R, and f̂ is locally integrable, then f(x0)= γ distributionally if and only if there exists k such that 1/2π limx→∫_ax_xf̂(t)e-ix0t dt=γ(C,k) for each a > 0, and similarly in the case when f̂ is a general distribution. Here (C,k) means in the Cesàro sense. This result generalizes the characterization of Fourier series of distributions with a distributional point value given in [5] by limxarrowσ-x
Publication Source (Journal or Book title)
Journal of Fourier Analysis and Applications
First Page
551
Last Page
576
Recommended Citation
Vindas, J., & Estrada, R. (2007). Distributional point values and convergence of fourier series and integrals. Journal of Fourier Analysis and Applications, 13 (5), 551-576. https://doi.org/10.1007/s00041-006-6015-z
