Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A note on global solvability of vector fields

Author: Jorge Hounie
Journal: Proc. Amer. Math. Soc. 94 (1985), 61-64
MSC: Primary 35F99; Secondary 35A99, 58G99
MathSciNet review: 781057
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider global solvability of complex vector fields on noncompact 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.

References [Enhancements On Off] (What's this?)

  • [1] F. Cardoso and J. Hounie, First order linear PDE's and uniqueness in the Cauchy problem, J. Differential Equations 33 (1979). MR 542672 (80h:35031)
  • [2] J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972). MR 0388464 (52:9300)
  • [3] J. Hounie, Globally hypoelliptic vector fields on compact surfaces, Comm. Partial Differential Equations 7 (1982). MR 652813 (83k:35025)
  • [4] L. Hörmander, Propagation of singularities and semi-global existence theorems for (pseudo-) differential operators of principal type, Ann. of Math. (2) 108 (1978).
  • [5] -, Pseudo-differential operators of principal type, Singularities in Boundary Value Problems, NATO Adv. Study Inst. Ser., Nijhoff, The Hague, 1981.
  • [6] D. Kim, Ph.D. Thesis, Rutgers Univ., 1981.
  • [7] B. Malgrange, Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier (Grenoble) 6 (1955-56). MR 0086990 (19:280a)
  • [8] H. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973). MR 0321133 (47:9666)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35F99, 35A99, 58G99

Retrieve articles in all journals with MSC: 35F99, 35A99, 58G99

Additional Information

Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society