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