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

Abstract

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.

37 pages. This is the second version. Title updated, new section added, misprints corrected. Some further changes might be performed in the next versions