An uncertainty principle for operators acting on Fock spaces

The PDE & Analysis seminar covers topics in PDE and analysis.

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27 Sep 2023 10:30am - 27 Sep 2023 11:30am
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Professor Sundaram Thangavelu (Indian Institute of Science)
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 Abstract: For each $ \lambda \in \R $ there is a Hilbert space of entire functions $ \mathcal{F}_\lambda(\C^{2n}) $ known as twisted Fock space. We show that within this space there is an algebra $ \mathcal{A}_\lambda(\C^{2n}) $ which is isometrically isomorphic to $ B(L^2(\R^n)).$ The map $ U $ defined by $ UF(z,w) =F(-iz,-iw) $ is a unitary operator on $ \mathcal{F}_\lambda(\C^{2n}) .$ We show that for any $ \varphi \in \mathcal{A}_\lambda(\C^{2n}),$ the function $ U\varphi $ can never be in $ \mathcal{A}_\lambda(\C^{2n})$ unless $ \varphi $ is a constant. This has an interpretation as an uncertainty principle for a class of operators of convolution type on the Fock space  $\mathcal{F}_\lambda(\C^{2n}).$ 

 This talk is based on my recent joint work with Rahul Garg.


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