Sub-Laplacians of holomorphic $L^p$-type on exponential solvable groups
| dc.creator | Hebisch, W. | |
| dc.creator | Ludwig, J. | |
| dc.creator | Mueller, D. | |
| dc.date | 2003-07-03 | |
| dc.date.accessioned | 2026-07-07T04:59:24Z | |
| dc.date.available | 2026-07-07T04:59:24Z | |
| dc.description | Let $L$ denote a right-invariant sub-Laplacian on an exponential, hence solvable Lie group $G$, endowed with a left-invariant Haar measure. Depending on the structure of $G$, and possibly also that of $L$, $L$ may admit differentiable $L^p$-functional calculi, or may be of holomorphic $L^p$-type for a given $p\ne 2$. By ``holomorphic $L^p$-type'' we mean that every $L^p$-spectral multiplier for $L$ is necessarily holomorphic in a complex neighborhood of some non-isolated point of the $L^2$-spectrum of $L$. This can in fact only arise if the group algebra $L^1(G)$ is non-symmetric. Assume that $p\ne 2$. For a point $l$ in the dual $\frak g ^*$ of the Lie algebra $\frak g$ of $G$, we denote by $Ω(l)=Ad^*(G)l$ the corresponding coadjoint orbit. We prove that every sub-Laplacian on $G$ is of holomorphic $L^p$-type, provided there exists a point $l\in \frak g ^*$ satisfying ``Boidol's condition'' (which is equivalent to the non-symmetry of $L^1(G)$), such that the restriction of $Ω(l)$ to the nilradical of $\frak g$ is closed. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/math/0307051 | |
| dc.identifier | http://arxiv.org/abs/math/0307051 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67970 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 22E30, 22E27, 43A20 | |
| dc.title | Sub-Laplacians of holomorphic $L^p$-type on exponential solvable groups | |
| dc.type | text |