An analogue of Hardy’s theorem for very rapidly decreasing functions on semi-simple Lie groups
An analogue of Hardy’s theorem for very rapidly decreasing functions on semi-simple Lie groups
We generalise a result of Hardy, which asserts the impossibility of a function and its Fourier transform to be simultaneously "very rapidly decreasing", to: (i) all noncompact, semi-simple Lie groups with one conjugacy class of Cartan subgroups; (ii) SL(2, R); and (iii) all symmetric spaces of the noncompact type.