We consider the numerical range of a bounded weighted composition operator $C_{\psi ,\phi }$ on the Fock space ${\mathcal{F}}^2$, where the entire function φ must have the form az + b with a and b in $\mathbb{C}$ and $|a|\le 1$. We obtain necessary and sufficient conditions for $\{\psi (p)a^n:n\text{is a non-negative integer}\}$ to be a subset of the interior of the numerical range of $C_{\psi ,\phi }$, where p is the fixed point of φ. We characterize when 0 belongs to the numerical range of a weighted composition operator and determine which weighted composition operators have numerical ranges with no corner points. Furthermore, we describe the corner points of the closure of the numerical range of a compact weighted composition operator. Moreover, we precisely determine the numerical range of $C_{\psi ,\phi }$ when $|a|=1$.

我们考虑有界加权合成算子的数值范围 $C_{\psi ，\phi }$ 在福克空间 ${\mathcal{F}}^2$，其中整个函数φ的形式必须为az  +  b，其中a和b为$\mathbb{C}$ 和 $|\mathrm{一种}|\le \mathrm{1个}$。我们获得了必要的充分条件$\{\psi （p）{\mathrm{一种}}^{ñ}：ñ\text{是一个非负整数}\}$ 成为内部数字范围的子集 $C_{\psi ，\phi }$，其中p是的固定点φ。我们表征0何时属于加权合成算子的数值范围，并确定哪些加权合成算子具有不带角点的数值范围。此外，我们描述了紧凑加权合成算子的数值范围的闭合角点。而且，我们精确地确定了$C_{\psi ，\phi }$ 什么时候 $|\mathrm{一种}|=\mathrm{1个}$。