Global solvability and hypoellipticity for evolution operators on tori and spheres.

In this paper, we investigate global properties of a class of evolution differential operators defined on a product of tori and spheres. We present a comprehensive characterization of global solvability and hypoellipticity, providing necessary and sufficient conditions that involve Diophantine conditions and the connectedness of sublevel sets associated with the coefficients of the operator. Furthermore, we recover well‐known results from existing literature and introduce novel contributions. [ABSTRACT FROM AUTHOR]