Infinite order $\Psi$DOs: Composition with entire functions, new Shubin-Sobolev spaces, and index theorem

Stevan Pilipović, Bojan Prangoski, Jasson Vindas

We study global regularity and spectral properties of power series of the Weyl quantisation $a^w$, where $a(x,\xi )$ is a classical elliptic Shubin polynomial. For a suitable entire…