Partial differential operators without right inverse on the tempered distributions
type: Item
instance of: scholarly article
title: Partial differential operators without right inverse on the tempered distributions
zbMATH Open document ID: 0696.35003
DOI: 10.1007/BF03322649
author: Jörg Krone
published in: Results in Mathematics
publication date: 1989-01-01T00:00:00Z
review text: If P(D) is a partial differential operator with constant coefficients P(D) is known to be surjective on \(S'({\mathbb{R}}^ n)\), the space of tempered distributions in n variables. The author proves that in general P(D) has no linear continuous right inverse. In particular, the Laplacian, the Cauchy-Riemann operator and the heat operator do not have a right inverse when \(n\geq 2\).
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35G05
Mathematics Subject Classification ID: 35E20
zbMATH DE Number: 4140233
zbMATH Keywords: right inverse
reviewed by: J. Frédéric Bonnans
MaRDI profile type: Publication
cites work: Q3843833
cites work: On the division of distributions by polynomials
cites work: Q5566770
cites work: Q5549261
cites work: Q5531982
cites work: Charakterisierung der Unterräume von \((s)\)
full work available at URL: https://doi.org/10.1007/bf03322649
OpenAlex ID: W2045491640
description: scientific article; zbMATH DE number 4140233