Generalized Whittaker functionals for real reductive groups

Let $(\pi,V)$ be a smooth representation of a real reductive group $G$. A generalized Whittaker functional is a continuous linear functional on $V$ that transforms by a character under a suitable unipotent subgroup. Such functionals play an important role in various applications, especially in the study of automorphic forms. In this talk I will describe a number of new results obtained in the direction.