Weighted composition operator on quaternionic Fock space

Abstract: In this paper, we study the weighted composition operator on the Fock space $\mf$ of slice regular functions. First, we characterize the boundedness and compactness of the weighted composition operator. Subsequently, we describe all the isometric composition operators. Finally, we introduce a kind of (right)-anti-complex-linear weighted composition operator on $\mf$ and obtain some concrete forms such that this (right)-anti-linear weighted composition operator is a (right)-conjugation. Specially, we present equivalent conditions ensuring weighted composition operators which are conjugate $\mathcal{C}{a,b,c}-$commuting or complex $\mathcal{C}{a,b,c}-$ symmetric on $\mf$, which generalized the classical results on $\mathcal{F}^2(\mathbb{C}).$ At last part of the paper, we exhibit the closed expression for the kernel function of $\mf.$