On the large time behavior of heat kernels on Lie groups
type: Item
instance of: scholarly article
title: On the large time behavior of heat kernels on Lie groups
zbMATH Open document ID: 1040.22004
DOI: 10.1215/S0012-7094-03-12024-4
author: Noël Lohoué
author: Georges Alexopoulos
published in: Duke Mathematical Journal
publication date: 2004-03-07T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.dmj/1082138586
review text: Let \(G\) be a connected noncompact semisimple Lie group with finite center and let \(E_1,\dots ,E_n\) be left invariant vector fields on \(G\) that satisfy Hörmander's condition; that is, they generate together with their successive Lie brackets \([E_{i_1},[ E_{i_2},[\dots, E_{i_{k-1}},E_{i_k}]\dots]]\) the tangent space \(T_xG\) at every point \(x\in G\). The corresponding sub-Laplacian is \(L=-(E_1^2+\dots ,+E_n^2)\). Denote by \(P_t(x,y)\) the associated heat kernel, that is the fundamental solution of the heat equation \((\frac{\partial}{\partial t}+L)u=0\). The authors study the large time behavior of the heat kernel \(P_t(x,y)\). The heat kernel \(P_t(x,y)\) is related to some other heat kernels defined by some subgroups \(A\) and \(N\) corresponding to some terms in the Iwasawa decomposition of the Lie algebra of \(G\). Next, some estimates for \(P_t(x,y)\) are obtained.
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 43A90
Mathematics Subject Classification ID: 60B99
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 2051860
zbMATH Keywords: Lie groups
zbMATH Keywords: heat kernels
zbMATH Keywords: sub-Laplacian
zbMATH Keywords: homogenization theory
reviewed by: Vasile Oproiu
MaRDI profile type: Publication
Wikidata QID: Q115240305
description: scientific article; zbMATH DE number 2051860