The Gibbs phenomenon for \(L_{\text{loc}}^1\) kernels
type: Item
instance of: scholarly article
title: The Gibbs phenomenon for \(L_{\text{loc}}^1\) kernels
zbMATH Open document ID: 0953.42006
published in: Journal of Approximation Theory
publication date: 1999-12-20T00:00:00Z
review text: The authors prove two theorems on the Gibbs phenomenon for multiple Fourier integrals in \(\mathbb{R}^n\), by reducing the problem to the one-dimensional case. In a third theorem they specify their results in the case of the Bochner-Riesz means of order \(\alpha> (n-3)/2\) of functions \(f: \mathbb{R}^n\to \mathbb{R}\) vanishing in \(\mathbb{R}^n\setminus C\) and smooth enough in \(C\), where the boundary of \(C\) is a smooth simple surface. The case when \(\alpha\leq(n- 1)/2\), the critical index, is especially remarkable.
Mathematics Subject Classification ID: 42B05
Mathematics Subject Classification ID: 42A16
zbMATH DE Number: 1356335
zbMATH Keywords: Gibbs phenomenon
zbMATH Keywords: multiple Fourier integrals
zbMATH Keywords: Bochner-Riesz means
author: Leonede De-Michele
author: Delfina Roux
reviewed by: Ferenc Móricz
MaRDI profile type: Publication
full work available at URL: jath.1998.3326
OpenAlex ID: W1514201745
cites work: The Gibbs phenomenon for multiple Fourier integrals
cites work: Q4386060
cites work: Q5640160
DOI: 10.1006/JATH.1998.3326
description: scientific article; zbMATH DE number 1356335