单叶解析函数强微分超属的最佳从属潘庆云(马鞍山师范高等专科学校经济与社会管理系,安徽马鞍山243000)摘要:复分析是研究复函数,特别是解析函数的数学理论,是古老而富有生命的数学分支之一,是一个经典的研究领域。近年来,越来越多的学者研究微分从属和强微分超属,其理论与方法不反应用于泛函分析、拓扑学、微分几何等数学分支,还涉及自然科学的诸多领域,如动力系统、量子力学、信号分析等。因此,对于微分从属和强微分超属的研究具有重要的理论意义与潜在的应用价值。学者OROSGI和OROSG首先引入并研究了强微分超属的概念及其性质,在此基础上,本文引入强微分超属和最佳从属子概念,研究并证明了在单叶解析函数单位圆盘边界未知的情况下,强微分超属的最佳从属子。关键词:强微分超属;最佳从属子;解析函数;单叶函数中图分类号:0174.5文献标志码:A文章编号:1007-4260(2023)01-0022-04BestSubordinationofStrongDifferentialHypergenusofUnivalentAnalyticFunctionsPANQingyun(DepartmentofEconomicandSocialManagement,MaanshanTeacher’sCollege,Maanshan243000,China)Abstract:Complexanalysisisthemathematicaltheoryofstudyingcomplexfunctions,especiallyanalyticfunctions.Itisoneoftheoldestandmostvitalbranchesofmathematicsandaclassicfieldofstudy.Recentyears,moreandmorescholarshavestudieddifferentialsubordinationandstrongdifferentialhypergenus.Theirtheoriesandmethodsarenotonlyappliedtofunctionalanalysis,topology,differentialgeometryandsoon,butalsotomanyfieldsofnaturalscience,suchasdynamicalsystem,quantummechanics,signalanalysisandsoon.Therefore,thestudyofdifferentialsubordinationandstronglydifferen-tialhypergenushasimportanttheoreticalsignificanceandpotentialapplicationvalue.ScholarsOROSGIandOROSGfirstin-troducedandstudiedtheconceptofstrongdifferentialhypergenusanditsproperties.Onthisbasis,thispaperintroducestheconceptsofstrongdifferentialhypergenusandthebestsubordinatesubgenus,andinvestigatesandprovesthebestsubordinateofstrongdifferentialhypergenusforunivalentanalyticfunctionswithunknownboundaryontheunitdisk.Keywords:strongdifferentialhypergenus;bestsubordinate;analyticfunction;univalentfunction几何函数理论作为复分析领域一个重要的...