2 problems

Conjecture on the $P-1$ Fischer pair. The operator $F_P$ is a bijection on $E(\mathbb{C}^{d})$; equivalently, $P-1$ and $P^{\ast}(D)$ form a Fischer pair for $E(\mathbb{C}^{d})$. T…

Let $P$ be a polynomial on $\mathbb{C}^{d}$, not necessarily homogeneous, and let $E(\mathbb{C}^{d})$ denote the space of entire functions $f:\mathbb{C}^{d}\to\mathbb{C}$. For a po…