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Equidistribution of Neumann data mass on triangles


Author: Hans Christianson
Journal: Proc. Amer. Math. Soc. 145 (2017), 5247-5255
MSC (2010): Primary 35F20
DOI: https://doi.org/10.1090/proc/13742
Published electronically: August 1, 2017
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Abstract: In this paper we study the behaviour of the Neumann data of Dirichlet eigenfunctions on triangles. We prove that the $ L^2$ norm of the (semi-classical) Neumann data on each side is equal to the length of the side divided by the area of the triangle. The novel feature of this result is that it is not an asymptotic, but an exact formula. The proof is by simple integrations by parts.


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Hans Christianson
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599
Email: hans@math.unc.edu

DOI: https://doi.org/10.1090/proc/13742
Received by editor(s): January 10, 2017
Published electronically: August 1, 2017
Communicated by: Joachim Krieger
Article copyright: © Copyright 2017 American Mathematical Society

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