On Theorems of Hardy, Gelfand–Shilov and Beurling for Semisimple Groups
On Theorems of Hardy, Gelfand–Shilov and Beurling for Semisimple Groups
In this paper we prove a strong version of Hardy’s theorem for the group Fourier transform on semisimple Lie groups which characterises the Fourier transforms of all functions satisfying Hardy type conditions. In the particular case of \mathit{SL}(2, ℝ) we characterise all such functions and conjecture that the same is …