ABOUT EIGENFUNCTIONS OF THE LAPLACIAN ON THE HYPERBOLIC DISC

By a theorem of Helgason, any eigenfunction of the Laplacian on the hy perbolic disc whose growth is atmost exponential is obtained by applyi ng a distribution on the circle to some power of the Poisson kernel. I n this Note we characterize the distributions leading to bounded eigen functions as those which are derivatives of Holder functions. (C) Acad emie des Sciences/Elsevier, Paris.