Powers of sub-Laplacian on step two nilpotent Lie groups
type: Item
instance of: scholarly article
title: Powers of sub-Laplacian on step two nilpotent Lie groups
zbMATH Open document ID: 1280.22014
author: Ajay Kumar
author: Mukund Madhav Mishra
published in: The Journal of Geometric Analysis
publication date: 2013-09-02T00:00:00Z
review text: \textit{G. B. Folland} [Bull. Am. Math. Soc. 79, 373--376 (1973; Zbl 0256.35020)] obtained a fundamental solution for the Kohn Laplacian on the Heisenberg group. Generalising Folland's result, the fundamental solution for the sub-Laplacian on a model step two nilpotent Lie group was obtained by \textit{R. Beals} et al. [Adv. Math. 121, No. 2, 288--345 (1996; Zbl 0858.43009)]. In this paper under review, the authors obtain an explicit and geometrical formula for the fundamental solution for higher order sub-Laplacians on a model step two nilpotent Lie group. Their results generalise the earlier known results for the fundamental solution for higher order sub-Laplacians on the Heisenberg group.
Mathematics Subject Classification ID: 22E25
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 32W50
Mathematics Subject Classification ID: 31C99
zbMATH DE Number: 6203584
zbMATH Keywords: fundamental solution
zbMATH Keywords: sub-Laplacian
zbMATH Keywords: Heisenberg group
zbMATH Keywords: nilpotent Lie groups
reviewed by: Sanjiv Gupta
MaRDI profile type: Publication
full work available at URL: s12220-012-9298-0
OpenAlex ID: W2057606637
Wikidata QID: Q115376875
cites work: The Green function of model step two hypoelliptic operators and the analysis of certain tangential Cauchy Riemann complexes
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cites work: Q3718948
DOI: 10.1007/S12220-012-9298-0
description: scientific article; zbMATH DE number 6203584