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

Müller, Detlef; Ricci, Fulvio

Ann. Math. (2) 143, No. 1, 1-49 (1996).

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.

Reviewer: P.Hillion (Le Vesinet)

MSC:

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

Keywords:

characteristics; solvability; differential operators; nilpotent Lie groups; vector field