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Differential operators of the first order with degenerate principal symbols. (English) Zbl 0823.35028

Bojarski, Bogdan (ed.) et al., Partial differential equations. Part 1. The 36th semester held at the Stefan Banach International Mathematical Center in Warsaw, Poland, from September 17 to December 17, 1990. Warsaw: Polish Academy of Sciences, Inst. of Mathematics. Banach Cent. Publ. 27, Part 1, 147-161 (1992).
This paper deals with the following differential operator on \(\mathbb{R}^ n\) \[ {\mathcal D}= \sum_{i,j=1}^ n a_{ij} x_ j {\partial \over {\partial x_ i}}+\mu, \] where \(A= (a_{ij})\) is a real-valued matrix and \(\mu\in \mathbb{C}^*\). The author proposes three different conditions on \(A\) and \(\mu\) sufficient for the surjectivity of \({\mathcal D}\) in the Schwartz space \(S' (\mathbb{R}^ n)\) of tempered distributions.
For the entire collection see [Zbl 0771.00021].

MSC:

35F05 Linear first-order PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)

Keywords:

Schwartz space
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