2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67938We prove local solvability for large classes of operators of the form $$ L=\sum_{j,k=1}^{2n}a_{jk}V_jV_k+iαU,$$ where the $V_j$ are left-invariant vector fields on the Heisenberg group satisfying the commutation relations $[V_j,V_{j+n}]=U$ for $1\le j\le n$, and where $A=(a_{jk})$ is a complex symmetric matrix with semi-definite real part. Our results widely extend all of the results for the case of non-real, semi-definite matrices $A$ known to date, in particular those obtained recently jointly with F. Ricci under Sjöstrand's cone condition.36 pagesClassical Analysis and ODEs35A05, 42A80text