Global regularity and stability in S-spaces for classes of degenerate shubin operators

Abstract

© 2009 Birkhäuser Verlag Basel/Switzerland. We study the uniform regularity and the decay at infinity for anisotropic tensor products of Shubin-type differential operators as well as for degenerate harmonic oscillators. As applications of our general results we obtain new theorems for global hypoellipticity for classes of degenerate operators in inductive and projective Gelfand–Shilov spaces.