We consider restrictions along closed geodesics and geodesic circles for eigenfunctions of the Laplace-Beltrami operator on a compact hyperbolic Riemann surface. We obtain a non-trivial bound on the L^2-norm of such restrictions as the eigenvalue tends to infinity. We use methods from the theory of automorphic functions and in particular the uniqueness of invariant functionals on irreducible unitary representations of PGL(2,R).
arXiv Mathematics e-prints
- Pub Date:
- March 2004
- Mathematics - Analysis of PDEs;
- Mathematics - Representation Theory
- An updated version of the text not intended for a publication for being obsolete. A remark on a bound for a period added.