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.


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