Generalized study of the operator $\alpha {\partial }^k{\bar{\partial }}^k+\beta {\bar{\partial }}^k+\gamma {\partial }^k+c$ in weighted Hilbert space $L^2(\mathbb{C},{\mathrm{e}}^{-|z{|}^2})$

Eramane Bodian, Winnie Ossete Ingoba, Souhaibou Sambou +2

By Hörmander's $L^2$-method, we study the operator $\alpha {\partial }^k{\bar{\partial }}^k+\beta {\bar{\partial }}^k+\gamma {\partial }^k+c$ for any order $k$ with $\alpha ,\beta ,\gamma \in \mathbb{R}$ such that $(…