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The Mean-Value Operator

  • Sigurdur Helgason
Chapter

Abstract

It is a consequence of a well-known theorem of Godement [1952] that if X is a two-point homogeneous space and u a harmonic function on X, i.e., Lu = 0, then u has the mean-value property

$$u = {M^{{r}}{u}}\quad {\text{for each}\;{ r}}.$$
(1)

Keywords

Bibliographical Note Normalize Haar Measure Real Analytic Manifold Riemannian Homogeneous Space Injectivity Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Sigurdur Helgason 2011

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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