Abstract. We study certain densely defined unbounded operators on the Fock space. These are the annihilation and creation operators of quantum mechanics in one complex variable. Whereas in several complex variables we have the $\partial$-operator and its adjoint $\partial^*$ acting on $(p, 0)$-forms with coefficients in the Fock space. We consider the corresponding $\partial$-complex and study spectral properties of the corresponding complex Laplacian $\tilde\Box = \partial \partial^* + \partial^* \partial$. Finally we study a more general complex Laplacian $\Box_D = D D^* + D^* D$, where $D$ is a differential operator of polynomial type.
The $\partial$-complex on the Fock space - Part I
17.04.2018 09:45 - 11:15
Location:
Seminar room 12, 2nd floor, Oskar-Morgenstern-Platz 1, 1090 Vienna