Analysis on Extended Heisenberg Group

Linear and Nonlinear Dissipative Dynamics

“…This relation allows us to show existence of a semigroup in infinite dimensions as well as uniform ergodicity in sup norm if additionally α > 0 ( [52], [16]). …”

Crystallographic Groups for Hormander Fields

“…Since our generator include jump type part, a nice method of [25] may not work. In [78] we proposed a strategy for Heisenberg group based on estimating the moments of coordinate functions and arguments of A. Grigor'yan [49]. It should be possible to generalise that to a class of free nilpotent Lie groups.…”

“…In [78] we have introduced an infinite Coxeter group on two generators associated to the Heisenberg group H 1 and studied related analysis. In this paper we present some possible outlook how that theory could be extended to include other noncompact Lie groups.…”

“…In this case one could check, similarly as in [78], (see also section 10), that such operator satisfy the following. Proposition 7.1 (Minimum Principle).…”

“…Using Hardy inequality together with quadratic form bound (10) one can dress this inequality up and obtain, (as in [78]), the following result. Theorem 7.5 (Log-Sobolev Coercive Bound).…”