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Quantum Ergodicity of Boundary Values of Eigenfunctions: A Control Theory Approach
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- Journal:
- Canadian Mathematical Bulletin / Volume 48 / Issue 1 / 01 March 2005
- Published online by Cambridge University Press:
- 20 November 2018, pp. 3-15
- Print publication:
- 01 March 2005
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- Article
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Consider
$M$, a bounded domain in 
${{\mathbb{R}}^{d}}$, which is a Riemanian manifold with piecewise smooth boundary and suppose that the billiard associated to the geodesic flow reflecting on the boundary according to the laws of geometric optics is ergodic. We prove that the boundary value of the eigen-functions of the Laplace operator with reasonable boundary conditions are asymptotically equidistributed in the boundary, extending previous results by Gérard and Leichtnam as well as Hassell and Zelditch, obtained under the additional assumption of the convexity of $M$.
