Title

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

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