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A representation-theoretic criterion for local solvability of left invariant differential operators on nilpotent Lie groups. (English) Zbl 0471.22009


MSC:

22E25 Nilpotent and solvable Lie groups
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
58J40 Pseudodifferential and Fourier integral operators on manifolds
22E60 Lie algebras of Lie groups
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
Full Text: DOI

References:

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[2] Универсал\(^{\приме}\)ные обертывающие алгебры., Издат. ”Мир”, Мосцощ, 1978 (Руссиан). Транслатед фром тхе Френч бы Ју. А. Бахтурин; Едитед бы Д. П. Žелобенко.
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[8] Mustapha Raïs, Solutions élémentaires des opérateurs différentiels bi-inbariants sur un groupe de Lie nilpotent, C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A495 – A498 (French). · Zbl 0236.46047
[9] Charles Rockland, Hypoellipticity on the Heisenberg group-representation-theoretic criteria, Trans. Amer. Math. Soc. 240 (1978), 1 – 52. · Zbl 0326.22007
[10] 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
[11] Lars Hörmander, Linear partial differential operators, Die Grundlehren der Math. Wissenschaften, Bd. 116, Springer-Verlag, Berlin and New York, 1963. · Zbl 0108.09301
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