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Global solvability of a class of involutive systems. (English) Zbl 0942.35011
The authors study a class of involutive systems of real vector fields on the $$N$$-dimensional torus. It is proved that global solvability is equivalent to an algebraic condition which uses Liouville forms.

##### MSC:
 35A30 Geometric theory, characteristics, transformations in context of PDEs
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##### References:
 [1] Bergamasco, A.P.; Cordaro, P.D.; Malagutti, P.A., Globally hypoelliptic systems of vector fields, J. funct. anal., 114, 267-285, (1993) · Zbl 0777.58041 [2] Bergamasco, A.P.; Cordaro, P.D.; Petronilho, G., Global solvability for certain classes of underdetermined systems of vector fields, Math. Z., 223, 261-274, (1996) · Zbl 0863.58062 [3] Cardoso, F.; Hounie, J., Global solvability of an abstract complex, Proc. amer. math. soc., 65, 117-124, (1977) · Zbl 0335.58015 [4] Hounie, J., Globally hypoelliptic and globally solvable first order evolution equations, Trans. amer. math. soc., 252, 233-248, (1979) · Zbl 0424.35030 [5] Treves, F., Study of a model in the theory of complexes of pseudodifferential operators, Ann. of math., 104, 269-324, (1976) · Zbl 0354.35067 [6] Treves, F., Hypo-analytic structures (local theory), (1992), Princeton University Press Princeton · Zbl 0787.35003
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