高阶空间中星形映射子类的托普利茨行列式与广义扎尔克曼猜想
Toeplitz determinant and generalized Zalcman conjecture for subclasses of starlike mappings in higher dimensions
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中文总结 AI 辅助
该研究针对复Banach空间单位球上的全纯映射，建立了三阶托普利茨行列式精确界与广义扎尔克曼泛函特例，将经典一维理论结果推广至高阶空间星形映射子类。
中文摘要 AI 辅助
在本手稿中，我们针对复Banach空间单位球上定义的一类全纯映射，建立了三阶托普利茨行列式的精确界以及广义扎尔克曼泛函的一个特例。所得估计作为特例给出了星形映射多个子类的对应界，同时为经典一维理论中的某些已知结果提供了高阶推广。
英文摘要
In this manuscript, we establish sharp bounds of the third-order Toeplitz determinant and a particular case of the generalized Zalcman functional for a class of holomorphic mappings defined on the unit ball in a complex Banach space. The obtained estimates yield corresponding bounds for several subclasses of starlike mappings as special cases and also provide higher-dimensional extensions of certain known results from the classical one-dimensional theory.
