Partial differential operators without right inverse on the tempered distributions
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 \(n\geq 2\).
scientific article; zbMATH DE number 4140233