In 1934, Ingham investigated the best possible decay admissible for the Fourier transforms $ \hat{f} $ of  compactly supported functions $ f $ on the real line. More precisely he proved the following: Suppose  $ \theta $ is a positive even function on $ \R $ decreasing to zero at infinity. Then there exist  compactly supported functions $ f $  for which $ |\hat{f}(y)| \leq C e^{-\theta(y)|y|} $  if and only if $ \int_1^\infty \theta(t)\, t^{-1}\, dt < \infty.$ In recent years there are several works investigating analogues of this theorem for  Fourier transforms on Lie groups and Riemannian symmetric spaces. In this talk we plan to describe some of the results. 

Afternoon tea will be provided at 3:30pm