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.
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]
On the solvability of homogeneous left-invariant differential operators on the Heisenberg group
M.M. PelosoSecondo
;
1997
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.
| File | Dimensione | Formato | |
|---|---|---|---|
|
1-s2.0-S0022123696930761-main.pdf
accesso riservato
Tipologia:
Publisher's version/PDF
Dimensione
281 kB
Formato
Adobe PDF
|
281 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
