ASYMPTOTICS OF SUBCOERCIVE SEMIGROUPS ON NILPOTENT LIE GROUPS
Nick Dungey, A. F. M. ter Elst, Derek W. Robinson, Adam Sikora, Communicated William, B. Arveson · TU/e Research Portal · 1998
Abstract. One can associate asymptotic approximates G ∞ and H ∞ with each nilpotent Lie group G and pure m-th order weighted subcoercive oper-ator H by a scaling limit. Then the semigroups S and S(∞) generated by H and H∞, on the spaces Lp(G), p ∈ [1,∞], satisfy lim t→∞ ‖St − S(∞)t ‖p→p = 0 if, and only if, G = G∞. If G 6 = G ∞ then lim t→∞ ‖Mf (St − S(∞)t)‖p→p = 0 on the spaces Lp(g), where g denotes the Lie algebra of G, and Mf denotes the operator of multiplication by any bounded function which vanishes at infinity.