关于一类单叶函数Schwarz导数的注记
A Note on the Schwarz Derivative of a Class of Univalent Functions
DOI: 10.12677/PM.2023.1312349, PDF,   
作者: 赵 林, 陆富强：贵州师范大学数学科学学院，贵州 贵阳
关键词: 单叶函数；Schwarz导数；Grunsky算子；Univalent Functions； Schwarz Derivative； Grunsky Operator
摘要: 利用Hilbert空间上的一个有界算子和单叶函数的性质，讨论一类单叶函数的Schwarz导数，并引入一类Grunsky系数。得到有界算子的内积与一类单叶函数Schwarz导数的关系，以及其Schwarz导数在复Hilbert空间下的范数与Grunsky系数的关系。
Abstract: By using a bounded operator on a Hilbert space and the properties of univalent functions, the Schwarz derivative of a class of univalent functions is discussed and a class of Grunsky coefficients is introduced. The relation between the inner product of a bounded operator and the Schwarz de-rivative of a class of univalent functions is obtained, as well as the relation between the norm of its Schwarz derivative in complex Hilbert space and the Grunsky coefficients.
文章引用：赵林, 陆富强. 关于一类单叶函数Schwarz导数的注记[J]. 理论数学, 2023, 13(12): 3365-3370. https://doi.org/10.12677/PM.2023.1312349

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