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Mean value extension theorems and microlocal analysis

Author: Eric Todd Quinto
Journal: Proc. Amer. Math. Soc. 131 (2003), 3267-3274
MSC (2000): Primary 58J05, 44A12; Secondary 35J05, 58J40
Published electronically: February 12, 2003
MathSciNet review: 1992868
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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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Additional Information

Eric Todd Quinto
Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155

Received by editor(s): May 1, 2002
Published electronically: February 12, 2003
Additional Notes: The author was partially supported by NSF grant 9877155 and later by grant 0200788
Communicated by: Andreas Seeger
Article copyright: © Copyright 2003 American Mathematical Society

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