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Global solvability for a class of complex vector fields on the two-torus. (English) Zbl 1065.35088
Summary: 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 Trèves. One-dimensional orbits diffeomorphic to the unit circle are allowed.

MSC:
35F05 Linear first-order PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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