Complex powers for a class of infinite order hypoelliptic operators

Abstract

© 2018, Institute of Mathematics. Polish Academy of Sciences. All rights reserved. We prove that the complex powers of a class of infinite order hypoelliptic pseudodifferential operators can always be represented as hypoelliptic pseudodifferential operators modulo ultra-smoothing operators. We apply this result to the study of semigroups generated by square roots of non-negative hypoelliptic infinite order operators. For this purpose, we derive precise estimates of the corresponding heat kernel.