Norms of geodesic restrictions for eigenfunctions on hyperbolic surfaces and representation theory

2004/03/25 by Reznikov, Andre · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0403437

Abstract

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 L²-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).

Cited by

• Restriction of eigenfunctions on products of spheres to submanifolds of maximal flats
• Spectral projection estimates restricted to uniformly embedded submanifolds
• The Geodesic Restriction Problem for Arithmetic Spherical Harmonics

Related

• Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
• Eigenfunctions restriction estimates for curves with nonvanishing geodesic curvatures in compact Riemannian surfaces with nonpositive curvature
• Weighted geodesic restrictions of arithmetic eigenfunctions
• Geodesic restrictions for the Casimir operator
• Refined L^p restriction estimate for eigenfunctions on Riemannian surfaces