Geodesic restrictions for the Casimir operator
Analysis of PDEs
2011-07-28 v2 Representation Theory
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.
Cite
@article{arxiv.1012.2853,
title = {Geodesic restrictions for the Casimir operator},
author = {Andre Reznikov},
journal= {arXiv preprint arXiv:1012.2853},
year = {2011}
}
Comments
Final version. To appear in J. of Functional Analysis