Communications in Partial Differential Equations · 2004 · 44 citations · 6 references
Natural SciencesMathematicsDifferential EquationsDynamical SystemsTopologyComplex GeometryLie GroupsOperator TheorySymplectic GeometryComplex Vector BundlesHolomorphic Vector BundlesSmooth Manifolds
Abstract We consider complex vector fields L on the two-torus. We regard L as an operator acting on smooth functions and study conditions for L to have a closed range. We also give conditions for the range of L to have finite codimension. Our results involve condition (P) of Nirenberg and Treves. One-dimensional orbits diffeomorphic to the unit circle are allowed.
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