几种复变量中一类全态映射的广义托普利兹决定因素

Pub Date : 2024-08-19 DOI:10.1007/s11785-024-01585-3

Qinghua Xu, Ting Jiang

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引用次数: 0

摘要

本文定义了广义托普利兹行列式，其项是具有 k 倍对称性的单位盘 \(\mathbb {U}\) 上全形函数的系数，然后建立了定义在复巴纳赫空间单位球上的一类全形映射的同次展开的相关项所形成的广义行列式的尖锐边界。这里提出的结果将概括吉里和库马尔（Complex Anal Oper Theory 17(6):86, 2023）给出的相应结果。

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The Generalized Toeplitz Determinants for a Class of Holomorphic Mappings in Several Complex Variables

In this paper, we define the generalized Toeplitz determinants whose entries are the coefficients of holomorphic functions on the unit disk \(\mathbb {U}\) with k-fold symmetric, and then we establish the sharp bounds of the generalized determinants formed over the related terms of homogeneous expansion of a class of holomorphic mappings defined on the unit ball of a complex Banach space. The results presented here would generalize the corresponding results given by Giri and Kumar (Complex Anal Oper Theory 17(6):86, 2023).

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