Summability of Cardinal Series and of Localized Fourier Series
Document Type
Article
Publication Date
12-1-1995
Abstract
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)
Applicable Analysis
First Page
271
Last Page
288
Recommended Citation
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
