Über eine Verheftung elliptischer Randwert‐Probleme

The paper presents a proof of the following‐theorem. Let M be a compact closed C ∞ ‐manifold which is the union of two submanifolds X + , X − with common boundary Y. Furthermore, let A:C ∞ (M, E) → C ∞ (M, F) be an elliptic pseudo‐differential operator ( E, F complex vector bundles on M ) with the transmission property with respect to Y. Then we can conclude: If + and − are elliptic boundary value problems for the restrictions of A to X + and X − respectively then we find an elliptic pseudodifferential operator S on Y with\documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm ind}A^{\rm +} + {\rm ind}A^ - = {\rm ind }A + {\rm ind}S. $$\end{document}