### 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 |
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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

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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.