Paley–Wiener–Schwartz theorems on quadratic CR manifolds

Given a quadratic CR manifold M embedded in a complex space, we study Paley–Wiener–Schwartz theorems for spaces of Schwartz functions and tempered distributions on M. We discuss the interpretation of the space of restrictions of entire functions of exponential growth to M in terms of their non-commutative Fourier transform. We provide some structure results of the considered entire functions of exponential growth in terms of the geometric properties of M.