Solvability in the large for a class of complex vector fields on the cylinder

Abstract

This work deals with global solvability of a class of complex vector fields of the form L = ∂ / ∂ t + ( a ( x , t ) + i b ( x , t ) ) ∂ / ∂ x , where a and b are real-valued C ∞ functions, defined on the cylinder Ω = R × S 1 . Relatively compact (Sussmann) orbits are allowed. The connection with Malgrangeʼs notion of L -convexity for supports is investigated.