We present some recent results, obtained jointly with Detlef Müller, on solvability of operators of the form
@article{JEDP_2000____A15_0, author = {Ricci, Fulvio}, title = {Solvability of second-order left-invariant differential operators on the {Heisenberg} group}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {15}, pages = {1--10}, publisher = {Universit\'e de Nantes}, year = {2000}, mrnumber = {2002c:22018}, zbl = {01808705}, language = {en}, url = {http://www.numdam.org/item/JEDP_2000____A15_0/} }
TY - JOUR AU - Ricci, Fulvio TI - Solvability of second-order left-invariant differential operators on the Heisenberg group JO - Journées équations aux dérivées partielles PY - 2000 SP - 1 EP - 10 PB - Université de Nantes UR - http://www.numdam.org/item/JEDP_2000____A15_0/ LA - en ID - JEDP_2000____A15_0 ER -
Ricci, Fulvio. Solvability of second-order left-invariant differential operators on the Heisenberg group. Journées équations aux dérivées partielles (2000), article no. 15, 10 p. http://www.numdam.org/item/JEDP_2000____A15_0/
[BG] Calculus on heisenberg manifolds, Annals of Math. Studies, Princeton Univ. Press, 1988. | MR | Zbl
and ,[DPR] Analysis of second order differential operators with complex coefficients on the heisenberg group, J. Reine Angew. Math. 464 (1995), 67-96. | MR | Zbl
, , and ,[Fo] Harmonic analysis in phase space, Annals of Math. Studies, Princeton Univ. Press, 1989. | MR | Zbl
,[FS] Estimates for the ∂b complex and analysis on the heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429-522. | MR | Zbl
and ,[G] Hypoellipticité pour une classe d'opérateurs pseudodifférentiels à caractéristiques doubles et paramétrix associées, C.R. acad. Sci. Paris A280 (1975), 1063-1065. | MR | Zbl
,[Hw] The oscillator semigroup, Proc. Symp. Pure Appl. Math. 48 (1988), 61-132. | MR | Zbl
,[Hö1] A class of hypoelliptic pseudodifferential operators with double characteristics, Math. Ann. 217 (1975), 165-188. | MR | Zbl
,[Hö2] Symplectic classification of quadratic forms, and general mehler formulas, Math. Zeitschr. 219 (1995), 413-449. | MR | Zbl
,[KM] Local solvability for a class of second order complex coefficient differential operators on the heisenberg group h2, preprint Mathematisches Seminar, Kiel (1999).
and ,[MPR1] On the solvability of homogeneous left-invariant differential operators on the heisenberg group, J. Funct. Anal. 148 (1997), 368-383. | MR | Zbl
, , and ,[MPR2] On local solvability for complex coefficient differential operators on the heisenberg group, J. Reine Angew. Math. 513 (1999), 181-234. | MR | Zbl
, , and ,[MR1] Analysis of second order differential operators on the heisenberg group. i, Invent. Math. 101 (1990), 545-582. | MR | Zbl
and ,[MR2] Analysis of second order differential operators on the heisenberg group. ii, J. Funct. Anal. 108 (1992), 296-346. | MR | Zbl
and ,[MT] Normal forms for involutive complex hamiltonian matrices under the real symplectic group, J. Reine Angew. Math. 513 (1999), 97-114. | MR | Zbl
and ,[MZ] Local solvability for positive combinations of generalized sub-laplacians on the heisenberg group, preprint Mathematisches Seminar, Kiel (1999). | Zbl
and ,[P] Non-elliptic laplace equations on nilpotent lie groups, Ann. Math. 119 (1984), 309-385. | MR | Zbl
,[Sj] Parametrices for pseudodifferential operators with multiple characteristics, Ark. för Math. 12 (1974), 85-130. | MR | Zbl
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