Norms of geodesic restrictions for eigenfunctions on hyperbolic surfaces and representation theory
Abstract
We consider restrictions along closed geodesics and geodesic circles for eigenfunctions of the LaplaceBeltrami operator on a compact hyperbolic Riemann surface. We obtain a nontrivial bound on the L^2norm 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).
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2004
 DOI:
 10.48550/arXiv.math/0403437
 arXiv:
 arXiv:math/0403437
 Bibcode:
 2004math......3437R
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Representation Theory
 EPrint:
 An updated version of the text not intended for a publication for being obsolete. A remark on a bound for a period added.