99-21   Berichtsreihe des Mathematischen Seminars der Universität Kiel

## Local solvability for positive combinations of generalized sub-Laplacians on the Heisenberg group

As one step in a program to understand local solvability of complex coefficient second order differential operators on the Heisenberg group in a complete way, solvability of operators of the form $\Delta_{S,\al}=\Delta_S +i\al U$, where the leading term $\Delta_S$ is a positive combination of generalized and degenerate generalized sub-Laplacians'', has been studied in a recent article \cite{MPR2} by M. Peloso, F. Ricci and the first named author. It was shown that there exists a discrete set of critical'' values $E\subset \CC$, such that solvability holds for $\al\not\in E$. The case $\al\in E$ remained open, and it is the purpose of this note to close this gap. Our results extend corresponding results in another article \cite{MPR1} by the above mentioned authors, by means of an even simplified approach which should allow for further generalizations.

Mathematics Subject Classification (1991): 22E30, 35A07, 35D05, 43A80

Bibliographical note: erscheint in Proc. Amer. Math. Soc.