Global hypoellipticity and solvability for a class of evolution operators in time-periodic weighted Sobolev spaces

We study the hypoellipticity and solvability properties of a class of time-periodic evolution operators, with coefficients globally defined on ${\mathbb{R}}^d$ and growing polynomially with respect to the space variable. To this aim, we introduce a class of time-periodic weighted Sobolev spaces, whose elements are characterised in terms of suitable Fourier expansions, associated with elliptic operators.