Proceedings of the American Mathematical Society

Author(s): Eric Todd Quinto
Journal: Proc. Amer. Math. Soc. 131 (2003), 3267-3274.
MSC (2000): Primary 58J05, 44A12; Secondary 35J05, 58J40
Posted: February 12, 2003
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 58J05, 44A12, 35J05, 58J40

Eric Todd Quinto
Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155
Email: Todd.Quinto@tufts.edu

DOI: 10.1090/S0002-9939-03-06926-0
PII: S 0002-9939(03)06926-0
Received by editor(s): May 1, 2002
Posted: February 12, 2003
Additional Notes: The author was partially supported by NSF grant 9877155 and later by grant 0200788
Communicated by: Andreas Seeger
Copyright of article: Copyright 2003, American Mathematical Society

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