On the Local solvability of a class of degenerate second order operators with complex coefficients

We study the local solvability of a class of operators with multiple characteristics. The class considered here complements and extends the one studied in [9], in that in this paper we consider some cases of operators with complex coefficients that were not present in [9]. The class of operators considered here ideally encompasses classes of degenerate parabolic and Schr\"odinger type operators. We will give local solvability theorems. In general, one has $L^2$ local solvability, but also cases of local solvability with better Sobolev regularity will be presented.