An uncertainty principle for operators acting on Fock spaces

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

schedule Date & time
Date/time
27 Sep 2023 | 10:30 - 11:30am
person Speaker

Speakers

Professor Sundaram Thangavelu (Indian Institute of Science)
next_week Event series
contact_support Contact

Content navigation

Description

Abstract: 

 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.

Location

145 Hanna Neumann Building, room 1.33

-35.275905261234, 149.1191726

Upcoming events in this series

Abstract technology background with connected dots
27 Sep 2023 | 10:30 - 11:30am

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

View the event
Abstract technology background with connected dots
26 Sep 2023 | 2 - 3pm

The Alt-Caffarelli problem and the Alt-Phillips problem are among the most well-studied elliptic free boundary problems

View the event