[1] |
M. F. Atiyah, Resolution of singularities and division of distributions, Comm. Pure Appl. Math. 23 (1970), 145 – 150. · Zbl 0188.19405 · doi:10.1002/cpa.3160230202 |
[2] |
I. N. Bernšteĭn, Analytic continuation of generalized functions with respect to a parameter, Funkcional. Anal. i Priložen. 6 (1972), no. 4, 26 – 40. |
[3] |
I. N. Bernšteĭn and S. I. Gel\(^{\prime}\)fand, Meromorphy of the function \?^{\?}, Funkcional. Anal. i Priložen. 3 (1969), no. 1, 84 – 85 (Russian). |
[4] |
Garrett Birkhoff, Representability of Lie algebras and Lie groups by matrices, Ann. of Math. (2) 38 (1937), no. 2, 526 – 532. · JFM 63.0090.01 · doi:10.2307/1968569 |
[5] |
W. Chang, Global solvability of invariant differential operators, Ph.D. Thesis, M.I.T., 1978. |
[6] |
Lawrence Corwin, A representation-theoretic criterion for local solvability of left invariant differential operators on nilpotent Lie groups, Trans. Amer. Math. Soc. 264 (1981), no. 1, 113 – 120. · Zbl 0471.22009 |
[7] |
Lawrence Corwin, Frederick P. Greenleaf, and Richard Penney, A general character formula for irreducible projections on \?² of a nilmanifold, Math. Ann. 225 (1977), no. 1, 21 – 32. · Zbl 0322.46049 · doi:10.1007/BF01364889 |
[8] |
L. Corwin and L. P. Rothschild, Necessary conditions for local solvability of homogeneous left invariant differential operators on nilpotent Lie groups, Acta Math. 147 (1981), no. 3-4, 265 – 288. · Zbl 0486.22006 · doi:10.1007/BF02392875 |
[9] |
Универсал\(^{\приме}\)ные обертывающие алгебры., Издат. ”Мир”, Мосцощ, 1978 (Руссиан). Транслатед фром тхе Френч бы Ју. А. Бахтурин; Едитед бы Д. П. Žелобенко. |
[10] |
Jacques Dixmier and Paul Malliavin, Factorisations de fonctions et de vecteurs indéfiniment différentiables, Bull. Sci. Math. (2) 102 (1978), no. 4, 307 – 330 (French, with English summary). · Zbl 0392.43013 |
[11] |
Michel Duflo, Opérateurs différentiels bi-invariants sur un groupe de Lie, Ann. Sci. École Norm. Sup. (4) 10 (1977), no. 2, 265 – 288 (French, with English summary). · Zbl 0353.22009 |
[12] |
Michel Duflo and David Wigner, Convexité pour les opérateurs différentiels invariants sur les groupes de Lie, Math. Z. 167 (1979), no. 1, 61 – 80 (French). · Zbl 0387.43007 · doi:10.1007/BF01215244 |
[13] |
G. B. Folland, A fundamental solution for a subelliptic operator, Bull. Amer. Math. Soc. 79 (1973), 373 – 376. · Zbl 0256.35020 |
[14] |
G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat. 13 (1975), no. 2, 161 – 207. · Zbl 0312.35026 · doi:10.1007/BF02386204 |
[15] |
Bernard Gaveau, Solutions fondamentales, représentations, et estimées sous-elliptiques pour les groupes nilpotents d’ordre 2, C. R. Acad. Sci. Paris Sér. A-B 282 (1976), no. 11, Ai, A563 – A566 (French, with English summary). · Zbl 0322.43016 |
[16] |
Roe W. Goodman, Nilpotent Lie groups: structure and applications to analysis, Lecture Notes in Mathematics, Vol. 562, Springer-Verlag, Berlin-New York, 1976. · Zbl 0347.22001 |
[17] |
P. C. Greiner, J. J. Kohn, and E. M. Stein, Necessary and sufficient conditions for solvability of the Lewy equation, Proc. Nat. Acad. Sci. U.S.A. 72 (1975), no. 9, 3287 – 3289. · Zbl 0308.35017 |
[18] |
L. Hörmander, Linear partial differential operators, Grundlehren Math. Wiss., vol. 116, Springer-Verlag, Berlin, 1963. · Zbl 0108.09301 |
[19] |
Lars Hörmander, On the division of distributions by polynomials, Ark. Mat. 3 (1958), 555 – 568. · Zbl 0131.11903 · doi:10.1007/BF02589517 |
[20] |
A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 57 – 110 (Russian). · Zbl 0090.09802 |
[21] |
Pierre Lévy-Bruhl, Résolubilité locale et globale d’opérateurs invariants du second ordre sur des groupes de Lie nilpotents, Bull. Sci. Math. (2) 104 (1980), no. 4, 369 – 391 (French, with English summary). · Zbl 0454.22004 |
[22] |
Hans Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math. (2) 66 (1957), 155 – 158. · Zbl 0078.08104 · doi:10.2307/1970121 |
[23] |
Gérard Lion, Hypoellipticité et résolubilité d’opérateurs différentiels sur des groupes nilpotents de rang 2, C. R. Acad. Sci. Paris Sér. A-B 290 (1980), no. 6, A271 – A274 (French, with English summary). · Zbl 0434.35026 |
[24] |
S. Łojasiewicz, Sur le problème de la division, Studia Math. 18 (1959), 87 – 136 (French). · Zbl 0115.10203 |
[25] |
A. I. Malcev, On a class of homogeneous spaces, Amer. Math. Soc. Translation 1951 (1951), no. 39, 33. |
[26] |
Calvin C. Moore and Joseph A. Wolf, Square integrable representations of nilpotent groups, Trans. Amer. Math. Soc. 185 (1973), 445 – 462 (1974). · Zbl 0274.22016 |
[27] |
L. Pukanzky, Leçons sur les représentations des groupes, Dunod, Paris, 1967. |
[28] |
L. Pukánszky, On the characters and the Plancherel formula of nilpotent groups, J. Functional Analysis 1 (1967), 255 – 280. · Zbl 0165.48603 |
[29] |
M. Raïs, Solutions élémentaires des opérateurs différentiels bi-invariants sur un groupe de Lie nilpotent, C. R. Acad. Sci. Paris Sér. A 273 (1971), 595-598. |
[30] |
Charles Rockland, Hypoellipticity on the Heisenberg group-representation-theoretic criteria, Trans. Amer. Math. Soc. 240 (1978), 1 – 52. · Zbl 0326.22007 |
[31] |
Linda Preiss Rothschild, Local solvability of left invariant differential operators on the Heisenberg group, Proc. Amer. Math. Soc. 74 (1979), no. 2, 383 – 388. · Zbl 0413.58021 |
[32] |
Linda Preiss Rothschild, Local solvability of second order differential operators on nilpotent Lie groups, Ark. Mat. 19 (1981), no. 2, 145 – 175. · Zbl 0485.35018 · doi:10.1007/BF02384475 |
[33] |
Linda Preiss Rothschild and David S. Tartakoff, Inversion of analytic matrices and local solvability of some invariant differential operators on nilpotent Lie groups, Comm. Partial Differential Equations 6 (1981), no. 6, 625 – 650. · Zbl 0477.58032 · doi:10.1080/03605308108820187 |
[34] |
Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. IX-X. Nouvelle édition, entiérement corrigée, refondue et augmentée, Hermann, Paris, 1966 (French). · Zbl 0962.46025 |
[35] |
François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. · Zbl 0171.10402 |
[36] |
Lawrence Corwin and Frederick P. Greenleaf, Character formulas and spectra of compact nilmanifolds, J. Functional Analysis 21 (1976), no. 2, 123 – 154. · Zbl 0319.22011 |