Some spectral properties of the canonical solution operator to $\bar{\partial }$ on weighted Fock spaces

Abstract

We characterize the Schatten class membership of the canonical solution operator to $\bar{\partial }$ acting on $L^2(e^{-2\varphi })$, where $\varphi$ is a subharmonic function with $\Delta \varphi$ a doubling measure. The obtained characterization is in terms of $\Delta \varphi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\varphi })$.

References in corpus (1)

• Interpolating and sampling sequences for entire functions