Wiener-Hopf theory and nonunimodular groups
type: Item
instance of: scholarly article
title: Wiener-Hopf theory and nonunimodular groups
zbMATH Open document ID: 0849.22008
published in: Journal of Functional Analysis
publication date: 1994-07-04T00:00:00Z
review text: Let \(G\) be a connected real nonunimodular (i.e. the modular function \(m(g) \not\equiv 1)\) Lie group. Let \(X_0, \dots, X_k\) be the left invariant fields on \(G\), let \(\Delta = \sum_{j \geq 1} X^2_j + X_0\) and \(T_t = e^{-t \Delta}\) be the left Laplacian and the left diffusion semigroup, respectively. Let \(p_t(x,y) = \phi_t (y^{-1} x)\) \((x, y \in G)\) be the corresponding ``left'' diffusion kernel. The main result of the paper is \[ \phi_t (g) = O(t^{-3/2}) \quad \forall g \in G, \quad t \to \infty. \]
Mathematics Subject Classification ID: 22E30
zbMATH DE Number: 599772
zbMATH Keywords: connected real Lie group
zbMATH Keywords: Laplacian
zbMATH Keywords: diffusion semigroup
author: N. Th. Varopoulos
MaRDI profile type: Publication
full work available at URL: jfan.1994.1039
OpenAlex ID: W2000934027
DOI: 10.1006/JFAN.1994.1039
description: scientific article; zbMATH DE number 599772