Expansion of automorphic functions

This paper proposes a method of expansion for automorphic functions on Lie groups, which generalizes the usual Fourier series expansion of automorphic functions on $SL_2(\mathbf R)/SO(2)$. Detailed consideration is given to the special case of the expansion of functions on $SL_3(\mathbf R)/SO(3)$, which are automorphic with respect to $SL_3(\mathbf Z)$.