On Gröchenig, Heil, and Walnut's proof of the local three squares theorem
type: Item
instance of: scholarly article
title: On Gröchenig, Heil, and Walnut's proof of the local three squares theorem
zbMATH Open document ID: 1021.42001
DOI: 10.1007/BF02384492
author: Kristian Seip
published in: Arkiv för Matematik
publication date: 2003-06-16T00:00:00Z
review text: The main result says the following. Consider strictly positive numbers \(r_2> r_1\) for which \(r_1/r_2 \notin Q\), and let \(\mu_k\) denote the characteristic function for the interval \([-r_k,r_k]\). Then the set of functions of the form \((g_1 \mu_1)*\mu_2+ \mu_1*(g_2\mu_2)\) with \(g_1,g_2\in L^2(-(r_1+r_2),r_1+r_2)\) is dense in \(L^2(-(r_1+r_2),r_1+r_2)\). A \(d\)-dimensional version is obtained by convolution.
Mathematics Subject Classification ID: 42A65
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1928892
zbMATH Keywords: completeness
zbMATH Keywords: locl three squares theorem
MaRDI profile type: Publication
cites work: Nonperiodic sampling and the local three squares theorem
cites work: Q4896037
full work available at URL: https://doi.org/10.1007/bf02384492
OpenAlex ID: W2078694098
description: scientific article; zbMATH DE number 1928892