Pizzetti's formula for H-type groups
type: Item
instance of: scholarly article
title: Pizzetti's formula for H-type groups
zbMATH Open document ID: 1185.35308
published in: Potential Analysis
publication date: 2009-11-04T00:00:00Z
review text: Let H be a H-type group, \(\Delta_H\) be the orthogonal sub-Laplacian on H. The paper under reviewing give a Pizzetti's formula on the H-type mean integral operator. An explicit formula for the \(k\)-th powers of \(\Delta_H\) is also given in proving the Pizzetti's formula. The corresponding results on the Heisenberg group, which is a special H-type group, can be found in the previous paper of the author [Potential Anal. 17, No. 2, 165--180 (2002; Zbl 1021.31003)]. And the Pizzetti type fromula in arbitrary Riemann manifolds, which don't contain the H-type groups, is established by \textit{A. Gray} and \textit{T. J. Willmore} [Proc. R. Soc. Edinb., Sect. A 92, 343--364 (1982; Zbl 0495.53040)]. The Pizzetti-type formula in the present paper may advantage the investigations and the computations of Numercial Analysis in the non-Euclidean setting of H-type and Heisenberg groups; and it may be applied in the study of asymptotic solutions of PDE and spherical harmonics in the non-Euclidean context.
Mathematics Subject Classification ID: 35R03
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 43A80
Mathematics Subject Classification ID: 41A58
Mathematics Subject Classification ID: 35C20
zbMATH DE Number: 5625027
zbMATH Keywords: Pizzetti's formula
zbMATH Keywords: H-type groups
zbMATH Keywords: sub-Laplacian
zbMATH Keywords: expansion of the mean integral
author: Andrea Bonfiglioli
reviewed by: Huoxiong Wu
MaRDI profile type: Publication
full work available at URL: s11118-009-9136-6
OpenAlex ID: W2108240687
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DOI: 10.1007/S11118-009-9136-6
description: scientific article; zbMATH DE number 5625027