GEOMETRIC TOOLS IN FUNCTION THEORY (AND THE HEISENBERG GROUP) V

5th and last. The horocycles in the hyperbolic disc carry the structure of a commutative group, hence a (crucial) notion of Fourier transform. In the complex ball, the corresponding (Heisenberg) group is noncommutative, hence its Fourier theory is more twisted, although not less crucial. We just give an overview of the subject.