一维及高维星形映射的二阶Toeplitz行列式

IF 1.6 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2025-06-29 DOI:10.1007/s13324-025-01098-y

Surya Giri

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引用次数: 0

摘要

本文建立了二阶Toeplitz行列式的尖锐估计，由\(\vert a_3^2 -a_4^2\vert \)给出，适用于星形函数的Ma-Minda类。通过推导在复Banach空间的单位球和\(\mathbb {C}^n\)中的单位多面盘上定义的全纯映射子类的尖锐界，将这些结果进一步推广到高维，从而得到了若干复变量中各一元映射子类的二阶Toeplitz行列式的相应估计。

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Second-Order Toeplitz Determinant for Starlike Mappings in One and Higher Dimensions

The present work establishes sharp estimates for second-order Toeplitz determinant, given by \(\vert a_3^2 -a_4^2\vert \), for the Ma-Minda class of starlike functions. These results are further extended to higher dimensions by deriving sharp bounds for a subclass of holomorphic mappings defined on the unit ball in a complex Banach space and the unit polydisc in \(\mathbb {C}^n\), leading to corresponding estimates for second-order Toeplitz determinants for various subclasses of univalent mappings in several complex variables.

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.