  In this paper we construct smooth cuspidal automorphic forms related to
integrable discrete series of a connected semisimple Lie group with finite
center for classical and adelic situation as an application of the theory of
Schwartz spaces for automorphic forms developed by Casselman. In the classical
situation, smooth cuspidal automorphic forms are constructed via an explicit
continuous map from the Frech\' et space of smooth vectors of a Banach
realization inside $L^1(G)$ of an integrable discrete series into the space of
smooth vectors of a strong topological dual of an appropriate Schwartz space.
