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Corwin, L. andGreenleaf, F. P., Rationally varying polarizing subalgebras in nilpotent Lie algebras.Proc. A.M.S. 81 (1981) no. 1, 27–32.
Corwin, L. andRotschhild, L. P., Necessary conditions for local solvability of homogeneous left invariant differential operators on nilpotent Lie groups (preprint).
Duflo, M., Operateurs differentiels bi-invariants sur un groupe de Lie.Ann. Scient. Ec. Norm. Sup.,10 (1977), 265–288.
Duflo, M. etRais, M., Sur l'analyse harmonique sur les groupes de Lie résolubles.Ann. Scient. Ec. Norm. Sup. 9 (1976), 107–144.
Folland, G. andStein, E. M., Estimates for the\(\overline {\partial _b } \) complex and analysis on the Heisenberg group.Comm. Pure Appl. Math. 27 (1974), 429–522.
Geller, D., Fourier analysis on the Heisenberg group (preprint).
Greiner, P., Kohn, J. J. andStein, E. M., Necessary and sufficient conditions for solvability of the Lewy equation.Proc. Nat. Acad. Sci. 72 (1975), no. 9, 3287–3289.
Grusin, V. V., On a class of hypoelliptic operators.Math. Sbornik 83 (125) (1970)3,Math USSR Sbornik 123 (1970), 458–475.
Helffer, B., Opérateurs invariants sur une classe de groupes nilpotents de rang 2 (manuscript).
Helffer, B. etNourrigat, J., Caractérisation des opérateurs hypoélliptiques homogènes invariants à gauche sur une groupe de Lie nilpotent gradué.Comm. P.D.E. 4 (8) (1979), 899–958.
Helgason, S.,Differential Geometry and Symmetric Spaces. Academic Press, New York 1962.
Helgason, S., The surjectivity of invariant differential operators on symmetric spaces, I.Ann. of Math. 98 (1973), 451–479.
Helgason, S., Solvability of invariant differential operators on homogeneous manifolds.CIME Seminar, Cremoneze, Rome (1975).
Hörmander, L., On the division of distributions by polynomials.Ark. Mat. 3 (1958), 555–568.
Hörmander, L.,Linear Partial Differential Operators. Springer-Verlag, Berlin, 1969.
Hörmander, L., Hypoelliptic, second-order differential equations.Acta Math. 119 (1967), 147–171.
Kirillov, A. A., Unitary representations of nilpotent Lie groups.Usp. Mat. Nauk. 17 (1962), 57–110.
Lévy-Bruhl, P., Resolubilité locale de certains opérateurs invariants du second ordre sur des groupes de Lie nilpotents de rang deux.Bull. Sci. Math. (to appear).
Lévy-Bruhl, P., Application de la formule de Plancherel à la resolubilité d'opérateurs invariants à gauche sur les groupes nilpotents d'ordre dueux (preprint).
Lévy-Bruhl, P., Resolubilité locale l'opérateurs homogènes sur des groupes de Lie nilpotents d'ordre deux (manuscript).
Lojasiewicz, S., Sur le probleme de division.Studia Math. 18 (1959), 87–136.
Pukanszky, L.,Leçons sur les Representations des Groups. Dunod, Paris, 1967.
Pukanszky, L., On the characters and the Plancherel formula of nilpotent groups.J. Func'l Anal. 1 (1967), 255–280.
Rais, M., Solutions élementaires des opérateurs differentiels bi-invariants sur un group de Lie nilpotent.C. R. Acad. Sci. Paris 273 (1971), 495–498.
Rockland, C., Hypoellipticity of the Heisenberg groups.Trans. Amer. Math. Soc. 240 (1978), no. 517, 1–52.
Rothschild, L. P., Local solvability of left-invariant differential operators on the Heisenberg group.Proc. A.M.S.,74 (1974), no. 2, 383–388.
Rothschild, L. P., andStein, E. M., Hypoelliptic differential operators and nilpotent groups.Acta Math. 137 (1976), 247–320.
Rothschild, L. P., andTartakoff, D., Inversion of analytic matrices and local solvability of some invariant differential operators on nilpotent Lie groups.Comm. P.D.E. 6 (1981), (6), 625–650.
Rouvière, F., Sur la résolubilite locale des opérateurs biinvariant.Ann Scuola Norm. Sup. Pisa (1976), 231–244.
Sato, M., Kawai, T. andKashiwara, M.,Micro-Functions and Pseudo-Differential Equations. Lecture Notes no. 287, Springer, New York, 1973.
Schwartz, L.,Theorie des Distributions, Tome I. Hermann & Cie, Paris (1950).
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Rothschild, L.P. Local solvability of second order differential operators on nilpotent Lie groups. Ark. Mat. 19, 145–175 (1981). https://doi.org/10.1007/BF02384475
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DOI: https://doi.org/10.1007/BF02384475