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

Key Points

• The aim is to understand the hypoellipticity and solvability of specific time-periodic evolution operators in weighted Sobolev spaces.
• Introduced a class of time-periodic weighted Sobolev spaces.
• Analyzed evolution operators with polynomially growing coefficients.
• Used Fourier expansions related to elliptic operators.
• Demonstrated that the studied operators exhibit hypoellipticity.
• Established conditions under which these operators are solvable in the new Sobolev spaces.