Closed ideals in convolution algebras and the Laplace transform
type: Item
instance of: scholarly article
title: Closed ideals in convolution algebras and the Laplace transform
zbMATH Open document ID: 0684.46045
author: Elizabeth Strouse
published in: Michigan Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: The convolution algebra \(L^ 1([0,1]^ n)\) on the n-fold product of the unit interval has an easily identified ideal structure when \(n=1\); the closed ideals are of the form \(M_{\beta}:=\{f:\) inf(ess.supp(f))\(\geq \beta \}\). This paper shows that this is not the case when \(n>1\). It then proceeds to establish a correspondence between the closed ideals of \(L^ 1([0,1]^ n)\) and the closed ideals in the quotient \(A_ 0^{(n)}/K\) of the algebra \(A_ 0^{(n)}\) consisting of the functions of n complex variables, continuous on the Cartesian product of n copies of the closed right half-plane, analytic on the interior of this set, vanishing at \(\infty\); K is an ideal generated by specified exponentials. The map establishing the correspondence is (essentially) the inverse Laplace transform.
reviewed by: Kjeld B. Laursen
Mathematics Subject Classification ID: 46J20
zbMATH DE Number: 4120813
zbMATH Keywords: convolution algebra
zbMATH Keywords: ideal structure
zbMATH Keywords: inverse Laplace transform
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003746
OpenAlex ID: W1998364016
DOI: 10.1307/MMJ/1029003746
description: scientific article; zbMATH DE number 4120813