2023年河北大学学报(自然科学版)2023第43卷第2期JournalofHebeiUniversity(NaturalScienceEdition)Vol.43No.2DOI:10.3969/j.issn.10001565.2023.02.003调和整映射的级和型乔金静1,田悦1,郑莉芳2(1.河北大学数学与信息科学学院,河北省机器学习与计算智能重点实验室,河北保定071002;2.石家庄铁道大学四方学院,河北石家庄051132)摘要:为讨论调和整映射的增长估计,研究其级和型,而级和型可以由其解析部分以及反解析部分的系数刻画.对于严格递增的正整数数列{nk}∞k=1,利用调和整映射的解析部分和反解析部分的nk阶导数在某一点的值,定义了2个量,且证明了这2个量分别与调和整映射的级和型几乎处处相等.关键词:整函数;调和整映射;级;型中图分类号:O174文献标志码:A文章编号:10001565(2023)02012706OrdersandtypesofharmonicentiremappingsQIAOJinjing1,TIANYue1,ZHENGLifang2(1.HebeiKeyLaboratoryofMachineLearningandComputationalIntelligence,CollegeofMathematicsandInformationScience,HebeiUniversity,Baoding071002,China;2.ShijiazhuangTiedaoUniversitySifangCollege,Shijiazhuang051132,China)Abstract:Inordertodiscussthegrowthestimatesofharmonicentiremappings,theorderandthetypeofharmonicentiremappingsarestudied,andtheycanbecharacterizedbythecoefficientsoftheanalyticpartsandanti-analyticparts.Forastrictlyincreasingsequenceofpositiveintegers{nk}∞k=1,twoquantitiesaredefinedbyusingthevaluesofnkorderderivativeoftheanalyticpartandanti-analyticpartofaharmonicentiremappingatacertainpoint,anditisprovedthatthesetwoquantitiesareequaltotheorderandthetypeoftheharmonicentiremapping,respectively,almosteverywhere.Keywords:entirefunction;harmonicentiremapping;order;type复平面C上的解析函数称为整函数.整函数的相关结果参见文献[1].设f是单连通区域D上的2次连续可微的复值函数,如果f满足Δf=4fzz=0,那么称f是调和映射.圆盘Dr={z:|z|
