Mean value extension theorems and microlocal analysis

Quinto, Eric

doi:10.1090/S0002-9939-03-06926-0

Mean value extension theorems and microlocal analysis
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by Eric Todd Quinto PDF

Proc. Amer. Math. Soc. 131 (2003), 3267-3274 Request permission

Abstract:

We use microlocal analysis to prove new mean value theorems for harmonic functions on harmonic manifolds and for solutions to more general differential equations. The equations we consider all satisfy spherical mean value equalities, at least locally. Microlocal analysis and the mean value property in a small set allows us to show that the solution to the differential equation in a small set is also a solution in a much larger set.

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