An operator heat semigroup and the Berger-Coburn theorem

Vishwa Dewage (Clemson U)

May 08. 2025, 14:00 — 14:30

Quantum harmonic analysis (QHA) is well-suited to study Toeplitz operators on the Fock space, as Toeplitz operators can be written as QHA convolutions.

We discuss an operator analog of the heat semigroup and then provide a very short proof of the well-known Berger-Coburn theorem for boundedness of Toeplitz operators (and also of the related theorems that discuss Schatten-class membership and compactness of Toeplitz operators). 

We also share some insights into the Berger-Coburn conjecture. We note that the analog of the Berger-Coburn conjecture that classifies Hilbert-Schmidt Toeplitz operators is indeed true.

This talk is based on joint work with Mishko Mitkovski.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Quantum Harmonic Analysis (Workshop)
Organizer(s):
Markus Faulhuber (U of Vienna)
Hans G. Feichtinger (U of Vienna)
Franz Luef (NTNU, Trondheim)