Complex powers for a class of infinite order hypoelliptic operators
Volume 529 / 2018
Dissertationes Mathematicae 529 (2018), 1-58
MSC: Primary 35S05; Secondary 46F05, 47D03.
DOI: 10.4064/dm770-11-2017
Published online: 5 April 2018
Abstract
We prove that the complex powers of a class of infinite order hypoelliptic pseudodifferential operators can always be represented as hypoelliptic pseudodifferential operators modulo ultrasmoothing 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.
