Submitted

Androulidakis I, Mohsen O, Yuncken R. A pseudodifferential calculus for maximally hypoelliptic operators and the Helffer-Nourigat conjecture. [Internet]. Submitted. Publisher's VersionAbstract

Given a filtration of the module of vector fields on a smooth manifold, we define a pseudodifferential calculus where the order of a vector field is given by the filtration. We show that pseudodifferential operators have a well-defined principal symbol for a subset of the unitary representations of the osculating groups. We prove a Rockland-type theorem, showing that the invertibility of the principal symbol is equivalent to maximal hypoellipticity. This answers affirmatively a conjecture due to Helffer and Nourrigat.

National and Kapodistrian University of Athens,

Department of Mathematics

(+30) 210-7276423

Panepistimiopolis Zografou

Athens, ZipCode 157-84

iandroul@math.uoa.gr