论文标题
加权伯格曼空间上的组成操作员的复杂对称性
Complex symmetry of composition operators on weighted Bergman spaces
论文作者
论文摘要
在本文中，我们研究了组成运算符的复杂对称性$ c_D = f \ circ ϕ $在加权伯格曼空间上引起的$ a^2_β（\ mathbb {d}），\β\ geq -1，$ by单位磁盘的分析自动图。我们的主要结果之一表明，每当$ c_ϕ $都是复杂的对称时，$ ϕ $在$ \ mathbb {d} $中具有固定点。我们的作品建立了复杂的对称性和循环性之间的密切关系。通过假设$β\ in \ mathbb {n} $和$ ϕ $是$ \ mathbb {d} $的椭圆形自动形态，而不是旋转，我们表明$ c_x $在$ 2（3+β）的订单大于$ 2（3+β）。$ 2（3+β）。$ 2（3+β）。$ 2（3+β）。
In this article, we study the complex symmetry of compositions operators $C_ϕf=f\circ ϕ$ induced on weighted Bergman spaces $A^2_β(\mathbb{D}),\ β\geq -1,$ by analytic self-maps of the unit disk. One of ours main results shows that $ϕ$ has a fixed point in $\mathbb{D}$ whenever $C_ϕ$ is complex symmetric. Our works establishes a strong relation between complex symmetry and cyclicity. By assuming $β\in \mathbb{N}$ and $ϕ$ is an elliptic automorphism of $\mathbb{D}$ which not a rotation, we show that $C_ϕ$ is not complex symmetric whenever $ϕ$ has order greater than $2(3+β).$
