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 journalArticle

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 Lp(G), p ∈ [1, ∞], satisfy limt→∞ ∥St - S(∞) tp→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.

Original languageEnglish
Pages (from-to)81-110
Number of pages30
JournalJournal of Operator Theory
Volume45
Issue number1
Publication statusPublished - 2001
Externally publishedYes

Keywords

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

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  • Cite this

    Dungey, N., Ter Elst, A. F. M., Robinson, D. W., & Sikora, A. (2001). Asymptotics of subcoercive semigroups on nilpotent Lie groups. Journal of Operator Theory, 45(1), 81-110.