Fusion Plasmas

On the decay of Fourier transforms

MSI Colloquium, where the school comes together for afternoon tea before one speaker gives an accessible talk on their subject

schedule Date & time
27 Sep 2023 4:00pm - 27 Sep 2023 5:00pm
person Speaker


Sundaram Thangavelu from Indian Institute of Science
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Brett Parker, Ian Le

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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



Seminar Room 1.33, Building 145, Science Road, ANU