Abstract: The Bargmann transform is a unitary operator from $L^2$ of the real line to the Fock space $F^2$ of the complex plane. Under the Bargmann transform, many classical operators on $L^2$ take fascinating new forms on the Fock space. The talk will focus on several examples of such operators, including the Fourier transform and the Hilbert transform. Motivated by the Hilbert transform, we also define a class of singular integral operators on the Fock space and discuss their boundedness.
