钱继晓

单叶亚纯螺旋象函数的刻画和积分表示

钱继晓

（南京理工大学 数学与统计学院，江苏 南京 210094）

黎曼映射定理为复变函数的性质提供了几何刻画；Carathéodory收敛定理把函数像域的收敛与函数的收敛性紧密联系起来。利用黎曼映射定理、极值原理和Carathéodory收敛定理，研究极点在原点和极点在点 (0<<1)的单叶亚纯螺旋象函数，得到了相应函数族的解析刻画和积分表示。

单叶函数；亚纯函数；螺旋象函数

1 引言

2 单叶亚纯螺旋象函数的刻画

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[1] BIEBERBACH L. Über einige extremal probleme im Gebiete der konformen abbildung[J]. Mathematische annalen, 1916, 77(2): 153–172.

[2] LOWNER K. Untersuchungen über schlichte konforme Abbildungen des Einheitskreises[J]. Mathematische annalen, 1923, 89(1): 103–121.

[3] GARABEDIAN P, SCHIFFER M. A proof of the Bieberbach conjecture for the fourth coefficient[J]. Journal of rational mechanics and analysis, 1955, 4: 427–465.

[4] PEDERSON R N. A proof of the Bieberbach conjecture for the sixth coefficient[M]. Carnegie institute of technology, department of mathematics, 1968.

[5] OZAWA M. An elementary proof of local maximality for a6[C]//Kodai Mathematical seminar reports, department of mathematics, Tokyo institute of technology, 1968, 20(4): 437–439.

[6] PEDERSON R N, SCHIFFERR M. A proof of the Bieberbach conjecture for the fifth coefficient[J]. Archive for rational mechanics and analysis, 1972, 45(3): 161–193.

[7] BRANGES L D, A proof of the Bieberbach conjecture[J]. Acta mathematica, 1985, 154(1): 137–152.

[8] PFALTZGRAFF J A, PINCHUK B. A variational method for classes of meromorphic functions[J]. J. Analyse math, 1971, 24: 101–150.

[9] OHNO R. Characterizations for concave functions and integral representations[J]. Topics in finite or infinite dimensional complex analysis, 2013: 203–216.

[10] POMMERENKE C. Boundary behaviour of conformal maps[M]. Springer science & business media, 2013.

Characterization and Integral Representation of Univalent Metamorphic Spirallike Functions

QIAN Ji-xiao

(School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing Jiangsu 210094, China)

The Riemann mapping theorem provides a geometric characterization for the properties of complex functions; the Carathéodory convergence theorem closely links the convergence of the function image field with the convergence of the function. Using the Riemann mapping theorem, the extreme value principle and the Carathéodory convergence theorem, the univalent meromorphic spirallike functions with the pole at the origin and the pole at the p point (0

univalent functions; meromorphic functions; spirallike functions

2022-03-20

江苏省研究生科研与实践创新计划项目 (KYCX21–0247)

钱继晓（1983—），男，江苏连云港人，硕士研究生，研究方向：复分析。

O174.52

A

2095-9249（2022）03-0011-05

〔责任编校：吴侃民〕