Sunto
In questa nota si considera il problema della risolubilità per operatori del secondo ordine, invarianti a sinistra e omogenei, sul gruppo di HeisenbergH n. Si presenta un approccio al problema basato sul prolungamento analitico dei coefficienti degli operatori, a partire dai risultati noti per il sub-Laplaciano. I dettagli sono contenuti in due articoli degli autori, in collaborazione con F. De Mari [DPR] e D. Müller [MPR].
This is a preview of subscription content, log in via an institution to check access.
Bibliografia
[BF]Beals, R. andFefferman, C.,On local solvability of linear partial differential equations, Annals Math.,97 (1973), 482–498.
[CR]Corwin, L. andRothschild, L.P.,Necessay conditions for local solvability of homogeneous left invariant operators on nilpotent Lie groups, Acta Math.,147 (1981), 265–288.
[DPR]De Mari, F., Peloso M.M. andRicci, F.,Analysis of second order differential operators with complex coefficients on the Heisenberg group, J. Reine Angew. Math.,464 (1995), 67–96.
[FS]Folland, G.B. andStein, E.M.,Estimates for the ∂ b complex and analysis on the Heisenberg group, Comm. Pure Appl. Math.,27 (1974), 429–522.
[GS]Gelfand, I.M. andShilov, G.E., Generalized Functions I, Academic Press, San Diego, 1964.
[H]Hörmander, L., The Analysis of Partial Differential Operators IV, Springer-Verlag, Berlin, 1985.
[H]Lewy, H.,An example of a smooth linear partial differential equation without solution, Ann. Math.,66 (1957), 155–158.
[M1]Müller, D.,A homogeneous, left-invariant, globally solvable differential operator on a nilpotent Lie group which has notempered fundamental solution, Proc. Amer. Math. Soc.,121 (1994), 307–310.
[M2]Müller, D.,Another example in the solvability theory of PDO's with double characteristic, Comm. Part. Diff. Eq.,20 (1995), 2165–2186.
[MPR]Müller, D., Peloso, M.M. andRicci, F.,On the solvability of homogeneous left-invariant differential operators on the Heisenberg group, (1995), preprint.
[MR1]Müller, D. andRicci, F.,Analysis of second order differential operators on Heisenberg groups. II J. Funct. Anal.,108 (1992), 296–346.
[MR2]Müller, D. andRicci, F.,Solvability for a class of doubly characteristic differential operators on 2-step nilpotent groups, Annals of Math.,143 (1996), 1–49.
[MR3]Müller, D. andRicci, F.,Solvability of second-order PDO's on nilpotent groups — a survey of recent results, The Journal of Geom. Anal.,3 (1993), 599–619.
[NT]Niremberg, L. andTreves, F.,On local solvability of linear partial differential equations, I, Necessary conditions; II Sufficient conditions; Corrections, Comm. Pure Appl. Math.,23;23;24 (1970; 1971), 1–38; 459–509; 279–288.
[R]Rothschild, L.P.,Local solvability of second order differential operators on nilpotent Lie groups, Ark. Mat.,19 (1981), 145–175.
[S]Stein, E.M.,An example on the Heisenberg group related to the Lewy operators, Inv. Math.,69 (1982), 209–216.
[W]Winfield, C. UCLA Ph. D. Dissertation, 1996.
Author information
Authors and Affiliations
Additional information
Conferenza tenuta da F. Ricci il 25 ottobre 1995
Rights and permissions
About this article
Cite this article
Peloso, M.M., Ricci, F. Sulla risolubilita' degli operatori differenziali invarianti sul gruppo di Heisenberg. Seminario Mat. e. Fis. di Milano 65, 321–333 (1995). https://doi.org/10.1007/BF02925263
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02925263