Summability of Cardinal Series and of Localized Fourier Series
We study the representation of distributions with support in the compact interval [-π,π] by localized Fourier series, i.e., series of the type [formula omitted] where H(π2 — θ2) is the characteristic function of the interval [-π,π]. We find necessary and sufficient conditions for the convergence or summability, in the Cesà or Abel senses, of such series. As a corolary we obtain necessary and sufficient conditions for the convergence and summability of cardinal series and conditions for the representation of certain functions by summable cardinal series. © 1995, Taylor & Francis Group, LLC. All rights reserved.
Publication Source (Journal or Book title)
Estrada, R. (1995). Summability of Cardinal Series and of Localized Fourier Series. Applicable Analysis, 59 (1-4), 271-288. https://doi.org/10.1080/00036819508840405