论文标题
真正的对称，统一和复杂的对称加权构图算子
Real Symmetric, Unitary, And Complex Symmetric Weighted Composition Operators On Bergman Spaces Of Polydisk
论文作者
论文摘要
在本文中，我们研究了可以在多迪斯克上集成正方形的分析功能的伯格曼空间的加权构图算子。我们以一般性的形式开发研究，这意味着不认为相应的加权成分算子是有限的。加权成分算子的特性，例如真实对称性，单位性，复杂对称性，以简单的代数术语充分表征，涉及其符号。事实证明，必须将具有对称结构的加权构图算子界定。我们还获得了一个有趣的结果，即实际的对称加权构图算子是复杂的对称对应的，对应于适应性且高度相关的共轭。
In this paper, we study weighted composition operators on Bergman spaces of analytic functions which are square integrable on polydisk. We develop the study in full generality, meaning that the corresponding weighted composition operators are not assumed to be bounded. The properties of weighted composition operators such as real symmetry, unitariness, complex symmetry, are characterized fully in simple algebraic terms, involving their symbols. As it turns out, a weighted composition operator having a symmetric structure must be bounded. We also obtain the interesting consequence that real symmetric weighted composition operators are complex symmetric corresponding an adapted and highly relevant conjugation.
