Equidistribution of Neumann data mass on triangles
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- by Hans Christianson PDF
- Proc. Amer. Math. Soc. 145 (2017), 5247-5255 Request permission
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.References
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Additional Information
- Hans Christianson
- Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599
- MR Author ID: 695231
- Email: hans@math.unc.edu
- Received by editor(s): January 10, 2017
- Published electronically: August 1, 2017
- Communicated by: Joachim Krieger
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 5247-5255
- MSC (2010): Primary 35F20
- DOI: https://doi.org/10.1090/proc/13742
- MathSciNet review: 3717953