On the solvability of homogeneous left-invariant differential operators on the Heisenberg group
Articolo
Data di Pubblicazione:
1997
Citazione:
On the solvability of homogeneous left-invariant differential operators on the Heisenberg group / D. Müller, M.M. Peloso, F. Ricci. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 148:2(1997), pp. 368-383. [10.1006/jfan.1996.3076]
Abstract:
We discuss the problem of solvability for the class of homogenoeus left-invariant operators □S,αon the Heisenberg groupHnintroduced by F. De Mari, M. M. Peloso, and F. Ricci. (1995,J. Reine Angew. Math.464, 67-96), whereS∈Sp(C,n) has a degenerated semi-definite real part, andα=±(n+2l),l=0,1,.... We completely characterize the solvable operators in this class. As a consequence we obtain that certain operators □S,αare solvable while their transposest□S,αare not. This is the case, for instance, for the operatorYZonH1, whereZ=X-iYis the unsolvable Lewy operator.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
2-step nilpotent groups; local solvability; lie-gropups; complex
Elenco autori:
D. Müller, M.M. Peloso, F. Ricci
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