Generalized Eigenfunction Expansions for Spectral Multiplicity One and Application in Analytic Number Theory

Robert M. Kauffman, Mayumi Sakata
2010 Rocky Mountain Journal of Mathematics  
We study generalized eigenfunction expansions of multiplicity one, obtaining precise convergence estimates. We apply the theory to the expansion for the Laplacian and Hecke operators on the fundamental domain for the modular group, where the convergence estimates are shown to be optimal.
doi:10.1216/rmj-2010-40-1-243 fatcat:6dxrh2qdorgundu63pvgiee6uy