On the solvability of vector fields with real linear coefficients
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- by François Treves PDF
- Proc. Amer. Math. Soc. 137 (2009), 4209-4218 Request permission
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
- Lojasiewicz, S., Notes, Institut Hautes Études, Bures-sur-Yvette, 1965.
- 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 348236
- François Trèves, Hypo-analytic structures, Princeton Mathematical Series, vol. 40, Princeton University Press, Princeton, NJ, 1992. Local theory. MR 1200459
- Treves, F., On planar vector fields with complex linear coefficients, to appear.
Additional Information
- François Treves
- Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903-2101
- Email: treves.jeanfrancois@gmail.com
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 4209-4218
- MSC (2000): Primary 35A07; Secondary 35F20
- DOI: https://doi.org/10.1090/S0002-9939-09-10033-3
- MathSciNet review: 2538582