TY - JOUR
T1 - Asymptotics of subcoercive semigroups on nilpotent Lie groups
AU - Dungey, Nick
AU - Ter Elst, A. F.M.
AU - Robinson, Derek W.
AU - Sikora, Adam
PY - 2001
Y1 - 2001
N2 - One can associate asymptotic approximates G∞ and H∞ with each nilpotent Lie group G and pure m-th order weighted subcoercive operator H by a scaling limit. Then the semigroups S and S(∞) generated by H and H∞, on the spaces Lp(G), p ∈ [1, ∞], satisfy limt→∞ ∥St - S(∞)t∥p→p = 0 if, and only if, G = G∞. If G ≠ G∞ then limt→∞ ∥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.
AB - One can associate asymptotic approximates G∞ and H∞ with each nilpotent Lie group G and pure m-th order weighted subcoercive operator H by a scaling limit. Then the semigroups S and S(∞) generated by H and H∞, on the spaces Lp(G), p ∈ [1, ∞], satisfy limt→∞ ∥St - S(∞)t∥p→p = 0 if, and only if, G = G∞. If G ≠ G∞ then limt→∞ ∥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.
KW - Asymptotics of semigroup kernels
KW - Asymptotics of semigroups
KW - Kernel bounds
KW - Nilpotent Lie groups
KW - Scaling
KW - Weighted subcoercive operators
UR - http://www.scopus.com/inward/record.url?scp=0039770164&partnerID=8YFLogxK
M3 - Article
SN - 0379-4024
VL - 45
SP - 81
EP - 110
JO - Journal of Operator Theory
JF - Journal of Operator Theory
IS - 1
ER -