Cusp forms for reductive symmetric spaces of split rank one

Abstract

For reductive symmetric spaces G / H G/H of split rank one we identify a class of minimal parabolic subgroups for which certain cuspidal integrals of Harish-Chandra–Schwartz functions are absolutely convergent. Using these integrals we introduce a notion of cusp forms and investigate its relation with representations of the discrete series for G / H G/H .