Title

Summability of Cardinal Series and of Localized Fourier Series

Authors

Ricardo Estrada

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

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