zbMATH — the first resource for mathematics

A note on global solvability of vector fields. (English) Zbl 0559.58032
We consider global solvability of complex vector fields on non-compact manifolds. The case of real vector fields had been considered by Malgrange, and Hörmander studied the complex case, assuming that the real and imaginary parts are everywhere linearly independent.

58J99 Partial differential equations on manifolds; differential operators
35F05 Linear first-order PDEs
Full Text: DOI
[1] Fernando Cardoso and Jorge Hounie, First-order linear PDEs and uniqueness in the Cauchy problem, J. Differential Equations 33 (1979), no. 2, 239 – 248. · Zbl 0377.35013 · doi:10.1016/0022-0396(79)90090-1 · doi.org
[2] J. J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972), no. 3-4, 183 – 269. · Zbl 0232.47055 · doi:10.1007/BF02392165 · doi.org
[3] J. Hounie, Globally hypoelliptic vector fields on compact surfaces, Comm. Partial Differential Equations 7 (1982), no. 4, 343 – 370. · Zbl 0588.35064 · doi:10.1080/03605308208820226 · doi.org
[4] L. Hörmander, Propagation of singularities and semi-global existence theorems for (pseudo-) differential operators of principal type, Ann. of Math. (2) 108 (1978). · Zbl 0396.35087
[5] -, Pseudo-differential operators of principal type, Singularities in Boundary Value Problems, NATO Adv. Study Inst. Ser., Nijhoff, The Hague, 1981. · Zbl 0459.35096
[6] D. Kim, Ph.D. Thesis, Rutgers Univ., 1981.
[7] Bernard Malgrange, Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier, Grenoble 6 (1955 – 1956), 271 – 355 (French). · Zbl 0071.09002
[8] Héctor J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171 – 188. · Zbl 0274.58002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.