Local solvability for a class of evolution equations

Motivated by the celebrated example of Y. Kannai of a linear partial differential operator which is hypoelliptic but not locally solvable, we consider a class of evolution operators with real-analytic coefficients and study their local solvability both in L2 and in the weak sense. In order to do so we are led to propose a generalization of the Nirenberg–Treves condition (ψ) which is suitable to our study.