An analogue of Hardy's theorem for very rapidly decreasing functions on semi-simple Lie groups
The main result is a generalization of a theorem of Hardy saying that a function on the real line and its Fourier transform cannot both be ``very rapidly decreasing'' to all noncompact semisimple Lie groups with finite center and one conjugacy class of Cartan subgroups. The result is also extended to \(\text{SL}(2,R)\) and to symmetric spaces of noncompact type. Such results can be viewed as uncertainty principles.
Fourier transforms of rapidly decreasing functions on semisimple Lie groups
scientific article; zbMATH DE number 1054235