ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 Mathematical Subject Classification: 35, 46 Domański, Paweł, A. Mickiewicz University, Poznań, Poland: Splitting of differential complexes. We consider exact sequences of continuous, open onto their images, linear operators:

(1)  0 ⟶ ker T_{0} ⟶ X_{0} ⟶^{T_{0}} X_{1} ⟶^{T_{1}} X_{2} ⟶^{T_{2}} …,

where all X_{i} are either equal to the spaces of smooth functions C^{∞}(Ω_{i}) or to the spaces of distributions D′(Ω_{i}), Ω_{i} ⊆ ℝ^{n} are open sets. Such complexes appear in the theory of systems of PDE’s when T_{i} are matrices of linear PDO with constant coefficients. We show by purely functional analytic methods that in the D′-case T_{i} : X_{i} → Im T_{i} has a continuous linear right inverse for every i ≥ 1. The same holds in the C^{∞}-case whenever T_{i} are matrices of convolution operators. This joint work with D. Vogt (Wuppertal) strengthens earlier results of Palamodov.