A theorem attributed to Beurling for the Fourier transform pairs asserts that for any nontrivial function $f$ on $\mathbb{R}$ the bivariate function $ f(x) \hat{f}(y) e^{|xy|} $ is never integrable over $ \mathbb{R}^2.$ Well known uncertainty principles such as theorems of Hardy, Cowlingâ€“Price etc. follow from this interesting result. In this talk we explore the possibility of formulating (and proving!) an analogue of Beurlingâ€™s theorem for the operator valued Fourier transform on the Heisenberg group.

The video of this talk is available on the IISc Math Department channel.

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Last updated: 26 Oct 2021