A nuclear approach to solving the equation \(Pu=f\) for an elliptic complex P
\textit{W. Koppelman}'s formula [Bull. Am. Math. Soc. 73, 554-556 (1967; Zbl 0186.138)] and \textit{F. Norguet}'s formula [Lect. Notes Math. 409, 1- 97 (1974; Zbl 0307.32004)] are generalized for an elliptic complex P. The tangent complex \(P_ B\) is associated to P and the problem of the exactness of the Mayer-Vietoris sequence of P and of the pair (\({\bar \Omega}\),c\(\Omega)\), \(\Omega\) being a domain with regular boundary, is analysed. The homotopy formulas are proved. Also, the compact support solution for the equation \(Pu=f\) is given. Finally the problem of the prolongation to the boundary for the complex P is formulated and analysed; the solution of the tangent equation on the boundary, \(P_ Bu^ 0=f^ 0\), is given. These results include as particular cases the corresponding results known for the Dolbeault complex \({\bar \partial}\) and de Rham complex \(\partial\).
scientific article; zbMATH DE number 3951651
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