最大模原理在无穷域中的运用及其推广
Application and Its extension of Maximum Modules Principle in Infinite Domains
胡文正1
作者信息
- 1. 华南师范大学数学科学学院,广东 广州 510631
- 折叠
摘要
本文运用最大模原理,研究了一类在复平面中以原点为对称中心的正n边形内连续且全纯的函数f.如果|f|在该正n边形内的上确界为M,且在该正n边形的某条边上的上确界为m,则可得出|f|在以原点为顶点和该条边为底边所形成的闭三角形内的上界.进而研究了一类在复平面中无穷条形区域以及无穷扇形区域内连续且全纯的函数f,并将它们推广到两种月牙形区域和两相切抛物线所形成的无穷区域,从而得到了一些重要的结论.
Abstract
This paper leverages the Maximum Modulus Principle to examine a specific class of continuous and analytic functions within a positively oriented n-polygon centered symmetrically at the origin on the complex plane,denoted as f.By assuming that the upper bound of|f|within the n-sided polygon is M,and the upper bound of|f|on a given edge of the n-sided polygon is m,we can derive the upper bound of|f|within a closed triangle,constructed using the origin as the vertex and this edge as the base.In addition,we also extend to a class of analytic functions in the infinite strip region and infinite sector region within the complex plane.Apart from the above,we also extend to two kinds of crescent-shaped regions and the infinite region formed by two parabolas,and some important conclusions are reached.
关键词
最大模原理/全纯函数/正方形区域/Schwarz对称原理/本性奇点Key words
maximum modulus principle/holomorphic function/square region/Schwarz symmetry principle/singularity of nature引用本文复制引用
基金项目
广东省自然科学基金面上项目(2021A1515010374)
出版年
2024
NETL
NSTL
万方数据