Geodesic restrictions for the Casimir operator

Andre Reznikov

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arXiv · 1012.2853

Geodesic restrictions for the Casimir operator

Andre Reznikov

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Abstract

We consider the hyperbolic Casimir operator C defined on the tangent sphere bundle SY of a compact hyperbolic Riemann surface Y. We prove a nontrivial bound on the L^2-norm of the restriction of eigenfunctions of C to certain natural hypersurfaces in SY. The result that we obtain goes beyond known (sharp) local bounds of L. Hormander.

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Andre Reznikov. 2011-07-27. Geodesic restrictions for the Casimir operator. https://arxiv.org/abs/1012.2853

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