Quantizations and global hypoellipticity for pseudodifferential operators of infinite order in classes of ultradifferentiable functions

Abstract

We study the change of quantization for a class of global pseudodifferential operators of infinite order in the setting of ultradifferentiable functions of Beurling type. The composition of different quantizations as well as the transpose of a quantization are also analysed, with applications to the Weyl calculus. We also compare global $\omega$-hypoellipticity and global $\omega$-regularity of these classes of pseudodifferential operators.