The heat kernel for generalized Heisenberg groups
type: Item
instance of: scholarly article
title: The heat kernel for generalized Heisenberg groups
zbMATH Open document ID: 0897.43007
DOI: 10.1007/BF02921603
author: Jennifer Randall
published in: The Journal of Geometric Analysis
publication date: 1998-10-06T00:00:00Z
review text: An explicit expression for the heat kernel \(h_t\) on a generalized Heisenberg or \(H\)-type group \(N\) is obtained. It is shown that \(h_t\) has an analytic extension \(h_z\), \(z\in \mathbb{C}\), \(\text{Re} (z)>0\), and that \(h_z\) is bounded in \(L^p(N)\). Estimates are obtained for \(\| h_z \|_p\), \(1\leq p\leq \infty\).
Mathematics Subject Classification ID: 43A80
Mathematics Subject Classification ID: 35A08
Mathematics Subject Classification ID: 58J35
zbMATH DE Number: 1160137
zbMATH Keywords: generalized Heisenberg group
zbMATH Keywords: heat semigroup
zbMATH Keywords: fundamental solution
zbMATH Keywords: \(L^p\)-estimates
zbMATH Keywords: \(H\)-type group
zbMATH Keywords: heat kernel
zbMATH Keywords: analytic extension
MaRDI profile type: Publication
cites work: Q5558293
cites work: Q4099504
cites work: Harmonic analysis on semigroups
cites work: Heat kernels for class 2 nilpotent groups
cites work: Q5820721
cites work: On a Generalisation of the Laplace Transformation
cites work: Lectures on partial differential equations. Delivered at the Indian Institute of Science, Bangalore. Notes by K. T. Joseph and S. Thangavelu
cites work: Subelliptic estimates and function spaces on nilpotent Lie groups
cites work: Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
cites work: The Radon transform
cites work: Hypoelliptic second order differential equations
cites work: The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group
cites work: Semi-Groups of Measures on Lie Groups
cites work: Representations of differential operators on a Lie group
cites work: Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Composition of Quadratic Forms
cites work: Q3671655
cites work: Commutative Algebras of Invariant Functions on Groups of Heisenberg Type
cites work: Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
cites work: Q5640160
cites work: Hardy-Littlewood theory for semigroups
full work available at URL: https://doi.org/10.1007/bf02921603
OpenAlex ID: W2019789100
description: scientific article; zbMATH DE number 1160137