A MEAN-VALUE THEOREM FOR SOME EIGENFUNCTIONS OF THE LAPLACE-BELTRAMI OPERATOR ON THE UPPER-HALF SPACE

被引：6

作者：

Eriksson, Sirkka-Liisa ^{[1
]}

Orelma, Heikki ^{[1
]}

机构：

[1] Tampere Univ Technol, Dept Math, FIN-33101 Tampere, Finland

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2011年 / 36卷 / 01期

关键词：

Laplace-Beltrami operator; mean-value theorem; hypermonogenic function; hyperbolic harmonic function;

D O I：

10.5186/aasfm.2011.3606

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study a mean-value property for solutions of the eigenvalue equation of the Laplace-Beltrami operator Delta(lb)h = -(n - 1)h with respect to the volume and the surface integrals on the Poincare upper-half space R-+(n+1) = {(x(0), ... ,x(n)) is an element of Rn+1 : x(n) > 0} with the Riemannian metric ds(2) = dx(0)(2)+dx(1)(2)+ ... +dx(n)(2)/x(n)(2) .

引用

页码：101 / 110

页数：10