## Solvability for a class of doubly characteristic differential operators on 2-step nilpotent groups.(English)Zbl 0841.22006

The authors discuss the solvability of left-invariant differential operators on connected, simply connected 2-step nilpotent Lie groups $$G$$ of the form $$L = \sum_{j, k = 1}^m a_{jk} V_j V_k + U$$ where $$v_1, \dots, v_m$$ are real, left-invariant vector fields, $$U$$ is a complex, left-invariant vector field and $$A = (a_{jk})$$ is a real symmetric matrix. They prove a theorem giving necessary and sufficient conditions for the solvability of these operators.

### MSC:

 22E25 Nilpotent and solvable Lie groups 35S05 Pseudodifferential operators as generalizations of partial differential operators 47G30 Pseudodifferential operators
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