Asymptotics of subcoercive semigroups on nilpotent Lie groups

Nick Dungey; A. F M Ter Elst; Derek W. Robinson; Adam Sikora

Asymptotics of subcoercive semigroups on nilpotent Lie groups

Nick Dungey^*, A. F M Ter Elst, Derek W. Robinson, Adam Sikora

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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 L_p(G), p ∈ [1, ∞], satisfy lim_t→∞ ∥S_t - S^(∞) _t∥_p→p = 0 if, and only if, G = G_∞. If G ≠ G_∞ then lim_t→∞ ∥M_f(S_t - S^(∞) _t)∥_p→p = 0 on the spaces L_p(g), where g denotes the Lie algebra of G, and M_f denotes the operator of multiplication by any bounded function which vanishes at infinity.

Original language	English
Pages (from-to)	81-110
Number of pages	30
Journal	Journal of Operator Theory
Volume	45
Issue number	1
Publication status	Published - 2001
Externally published	Yes

Keywords

Asymptotics of semigroup kernels
Asymptotics of semigroups
Kernel bounds
Nilpotent Lie groups
Scaling
Weighted subcoercive operators

Cite this

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title = "Asymptotics of subcoercive semigroups on nilpotent Lie groups",

abstract = "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.",

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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

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M3 - Article

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SN - 0379-4024

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JO - Journal of Operator Theory

JF - Journal of Operator Theory

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ER -

Asymptotics of subcoercive semigroups on nilpotent Lie groups

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Keywords

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