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Loewner differential equations for univalent functions

Title
Loewner differential equations for univalent functions
Authors
정지영
Issue Date
1997
Department/Major
대학원 수학과
Keywords
Loewnerdifferential equationsunivalent functionsMathematics
Publisher
The Graduate School, Ewha Womans University
Degree
Master
Abstract
단엽함수족과 관련된 Loewner chain을 소개하고, Loewner 미분 방정식과 연관하여 Loewner chain이 되기 위한 필요충분조건을 연구한다. 또한, 이 미분방정식을 단엽함수족에서 나오는 유계 성질들을 찾는데 적용시킨다. 더 나아가, 단엽함수족의 역계수 문제에 대한 Baernstein의 방법을 살펴보고, 이 방법을 이용하여 starlike 함수족에 대한 Loewner 정리의 다른 증명을 제시한다.;In this thesis, we introduce a Loewner chain which is related to the normalized univalent functions anh study the necessary and sufficient conditions for Loewner chain in connection with the Loewner Differential Equations. We apply the Loewner Differential Equations to derive some growth estimates for univalent functions. Moreover, we study the Baernstein's method for the inverse coefficient problems in the class of univalent functions and give an alternate proof of Loewner's Theorem for starlike functions by using Baernstein's technique.
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일반대학원 > 수학과 > Theses_Master
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