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Solvability of dissipative second order left-invariant differential operators on the Heisenberg group

Detlef Mueller
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Abstract

We 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.

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Detlef Mueller. 2003-07-01. Solvability of dissipative second order left-invariant differential operators on the Heisenberg group. https://arxiv.org/abs/math/0307002

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