Pointwise bounds for L² eigenfunctions on locally symmetric spaces

2010/05/17 by Ji, Lizhen, Weber, Andreas
#Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1005.2980

Abstract

We prove pointwise bounds for L² eigenfunctions of the Laplace-Beltrami operator on locally symmetric spaces with ℚ-rank one if the corresponding eigenvalues lie below the continuous part of the L² spectrum. Furthermore, we use these bounds in order to obtain some results concerning the L^p spectrum.

Related

• Characterization of almost L^p-eigenfunctions of the Laplace-Beltrami\n operator
• Absence of principal eigenvalues for higher rank locally symmetric spaces
• Restriction of eigenfunctions on products of spheres to submanifolds of maximal flats
• Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
• Sharp local L^p estimates for the Hermite eigenfunctions