AI 中文总结
该研究未预先指定共轭算子，借助再生核与生成函数刻画Fock空间上有界复对称加权复合算子，所得共轭算子多为反线性高斯积分算子，部分为加权复合共轭算子。
AI 中文摘要
我们对Fock空间\\(\mathcal F_{\alpha}^{2}\\)上所有有界复对称加权复合算子进行刻画，未预先指定共轭算子。该方法使用再生核与两个生成函数，这两个函数的泰勒系数分别是该算子及其伴随算子的特征向量。由构造得到的共轭算子是反线性高斯积分算子，部分为加权复合共轭算子，其余则不是。
英文摘要
We characterize all bounded complex symmetric weighted composition operators on the Fock space \(\mathcal F_α^{2}\), without prescribing a conjugation a priori. Our approach uses reproducing kernels and two generating functions. The Taylor coefficients of these functions are eigenvectors of the operator and its adjoint, respectively. The conjugations arising from our construction are anti-linear Gaussian integral operators. Some of them are weighted composition conjugations, whereas others are not.
