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)



On the solvability of vector fields with real linear coefficients

Author: François Treves
Journal: Proc. Amer. Math. Soc. 137 (2009), 4209-4218
MSC (2000): Primary 35A07; Secondary 35F20
Published electronically: July 31, 2009
MathSciNet review: 2538582
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The following result is proved: for a vector field with real linear coefficients to be locally solvable in $ \mathbb{R}^{n}$ it is necessary and sufficient that not all its orbits have a compact closure in the complement of the critical set of the vector field.

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

  • [Lojasiewicz, 1965] Lojasiewicz, S., Notes, Institut Hautes Études, Bures-sur-Yvette, 1965.
  • [Miwa, 1973] Tetsuji Miwa, On the existence of hyperfunction solutions of linear differential equations of the first order with degenerate real principal symbols, Proc. Japan Acad. 49 (1973), 88–93. MR 0348236
  • [Treves, 1992] François Trèves, Hypo-analytic structures, Princeton Mathematical Series, vol. 40, Princeton University Press, Princeton, NJ, 1992. Local theory. MR 1200459
  • [Treves, 2009] Treves, F., On planar vector fields with complex linear coefficients, to appear.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35A07, 35F20

Retrieve articles in all journals with MSC (2000): 35A07, 35F20

Additional Information

François Treves
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903-2101

Keywords: Vector fields, local solvability, foliations
Received by editor(s): April 14, 2009
Received by editor(s) in revised form: April 29, 2009
Published electronically: July 31, 2009
Communicated by: Bryna Kra
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society