We propose a new approach to the study of eigenfunctions of the Laplace-Beltrami operator on a Riemann surface of curvature - 1. It is based on Frobenius reciprocity from the theory of automorphic functions. We determine Sobolev class of arising automorphic functionals and discuss some applications.
|Translated title of the contribution||Sobolev norms of automorphic functionals and Fourier coefficients of cusp forms|
|Number of pages||6|
|Journal||Comptes Rendus de l'Academie des Sciences - Series I: Mathematics|
|State||Published - Jul 1998|