Bargmann and Fock meet Hardy: an uncertainty principle for operators

Speaker: Professor Sundaram Thangavelu 
Affiliation: Indian Institute of Science

Abstract

Heisenberg uncertainty principle in Quantum Mechanics states that the position and momentum of a moving particle cannot both be measured simultaneously. Viewed as an interesting property of the Fourier transform, this principle has several different manifestations in the realm of Fourier Analysis, including a theorem of Hardy studied extensively by harmonic analysts. Quite unexpectedly, this principle of Hardy shows its ugly head (or charming face) in connection with the boundedness of certain convolution type operators on the Fock space. The key player is Bargmann who connects Schr\"odinger with Fock and as expected, Hermite has his own role to play. We plan to describe this story with as little details as possible.