复Banach空间上一类双全纯映射的Hankel、Toeplitz、Hermitian - Toeplitz行列式与Zalcman泛函
Hankel, Toeplitz, Hermitian--Toeplitz Determinants and the Zalcman Functional for a Class of Biholomorphic Mappings on Complex Banach Spaces
浏览论文内容
中文总结 AI 辅助
研究复Banach空间上一类双全纯映射的多种行列式及泛函，受单位圆盘解析函数结果启发，建立Banach空间类似物，将单变量不等式推广到高维，为相关类提供对应。
中文摘要 AI 辅助
本文研究复Banach空间上一类归一化双全纯映射的第二Hankel行列式、Toeplitz行列式、Hermitian - Toeplitz行列式以及广义Zalcman泛函。受单位圆盘内相应解析函数类近期结果启发，建立了这些行列式估计的Banach空间类似物。结果将Allu、Lecko和Thomas的单变量不等式推广到复Banach空间情形，为对应于$\mathcal{F}_{O}(\lambda)$的类提供了高维对应。
英文摘要
In this paper, we investigate the second Hankel determinant, Toeplitz determinants, Hermitian--Toeplitz determinants and the generalized Zalcman functional for a class of normalized biholomorphic mappings on complex Banach spaces. Motivated by recent results for the corresponding class of analytic functions in the unit disk, we establish Banach space analogues of these determinant estimates. Our results extend the one-variable inequalities of Allu, Lecko and Thomas \cite{ALT2022} to the setting of complex Banach spaces, thereby providing higher-dimensional counterparts for the class corresponding to $\mathcal{F}_{O}(λ)$.
发表机构
- Amity School of Applied Sciences, Amity University Mumbai（安比蒂应用科学学院，孟买安比蒂大学）
- Department of Mathematics, Raiganj University（拉甘杰大学数学系）
机构由 AI 辅助整理，请以论文原文为准。
