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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
Posted:
July 31, 2009
MathSciNet review:
2538582
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Abstract: The following result is proved: for a vector field with real linear coefficients to be locally solvable in  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.
- [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
(50 #734)
- [Treves, 1992]
François
Trèves, Hypo-analytic structures, Princeton
Mathematical Series, vol. 40, Princeton University Press, Princeton,
NJ, 1992. Local theory. MR 1200459
(94e:35014)
- [Treves, 2009]
Treves, F., On planar vector fields with complex linear coefficients, to appear.
- [Lojasiewicz, 1965]
- Lojasiewicz, S., Notes, Institut Hautes Études, Bures-sur-Yvette, 1965.
- [Miwa, 1973]
- Miwa, T., 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 (50:734)
- [Treves, 1992]
- Treves, F., Hypo-analytic Structures, Local Theory, Princeton University Press, Princeton, NJ, 1992. MR 1200459 (94e:35014)
- [Treves, 2009]
- Treves, F., On planar vector fields with complex linear coefficients, to appear.
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Additional Information
François Treves
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903-2101
Email:
treves.jeanfrancois@gmail.com
DOI:
http://dx.doi.org/10.1090/S0002-9939-09-10033-3
PII:
S 0002-9939(09)10033-3
Keywords:
Vector fields,
local solvability,
foliations
Received by editor(s):
April 14, 2009
Received by editor(s) in revised form:
April 29, 2009
Posted:
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.
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