The Mean-Value Operator

  • Sigurdur Helgason


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

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


Bibliographical Note Normalize Haar Measure Real Analytic Manifold Riemannian Homogeneous Space Injectivity Result 
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Copyright information

© Sigurdur Helgason 2011

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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