Crystallographic Groups for Hormander Fields

Abstract

Abstract. This is a preview paper on Crystallographic Groups of Hörmander Fields. We describe an emerging picture in analysis of extended groups. In particular, we introduce and provide examples of Crystallographic Groups associated to a Hörmander system of fields as well as discuss some related analysis.

Linear and Nonlinear Dissipative Dynamics

“…Remark 2 A theory of dissipative semigroups generated by Dunkl type operators associated to noncommutative groups was recently developed in [52] and [53] .…”

“…That is S jk is a reflection in the sense of [52], [53] (in the direction of "tangent vector" δ l ). Using this we can introduce the following generalised derivations…”

“…We remark that in general the operators T l may not commute (and thus we are in general setup of [53]). …”