覆盖结果与扰动Roper-Suffridge算子
Covering results and perturbed Roper--Suffridge operators
摘要：
本文对Roper-Suffridge型扩张算子作了进一步的研究。对于复平面的开单位圆盘上给定的非正规螺旋函数（关于内部点或边界点），在一类巴拿赫空间中构造了扰动扩张算子，并证明了这些算子保持螺旋性质.此外，我们还给出了半群生成元的扩张算子。我们使用一种新的几何方法的基础上的螺旋状映射和单参数连续半群之间的联系。事实证明，下面建立的新的一维覆盖结果对我们的研究至关重要。
英文摘要：
This work is devoted to the advanced study of Roper--Suffridge type extension operators. For a given non-normalized spirallike function (with respect to an interior or boundary point) on the open unit disk of the complex plane, we construct perturbed extension operators in a certain class of Banach spaces and prove that these operators preserve the spirallikeness property. In addition, we present an extension operator for semigroup generators. We use a new geometric approach based on the connection between spirallike mappings and one-parameter continuous semigroups. It turns out that the new one-dimensional covering results established below are crucial for our investigation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
