29436.有界解析函數(shù)與cantor邊界性質(zhì)的相關(guān)問(wèn)題

1、分類(lèi)號(hào)Q里型學(xué)校代碼10542有界解析函數(shù)與Cantor邊界性質(zhì)的相關(guān)問(wèn)題SomeproblemsrelatedfunctionsandCantortoboundedanalyticboundarybehavior研究生姓名：戴堡登指導(dǎo)教師姓名、職稱(chēng)：董塹墨墊塑研究方向：分形幾何與塹坌塹湖南師范大學(xué)學(xué)位評(píng)定委員會(huì)辦公室二零一四年五月ABSTRACTThepointcutofinterdisciplinaryresearchofcompl

2、exanalysisandfractalgeometryisthestudyofCauchytransformofselfsimilarmeasure，WhichalsoforcedthestudyofCantorboundarybehavior(CBB)ofanalyticfunctionsTheconceptofCBBWasproposedbyprofessorDongandLauwhichiscloselyrelatedwithT

3、opologyandMeasuretheoryItsstudyaddvitalityforclassicalcomplexanalysisandopenupanewdirectionforfractalgeometryresearchInthisthesis，weselecttopicsfromabovefieldsandmainlyconsidertwoproblems：1TheCBBofCanchytransformofthe3le

4、velSierpinskigasket2TheboundarybehavioroftheproperholomorphicmappingsonboundedsimplyconnecteddomainsNaturally’wesplitthethesisintofourChapters：Chapter1isintroduction；Chapter2ispreliminary；InChapter3，westudytheCauchytrans

5、formFonthe3levelSierpinskigasketKInthischapter，weobtaintheestimationofFnearsomeboundarypointsoftheunboundedconnectedcomponent△oofC|KandstudytheasymptoticgrowthofF7nearthesepoints。Makinguseoftheseresults，weprovethatFhasCa

6、ntorboundarybehavior(CBBlonAoInaddition，weconsidertheLaurentexpansionofFandfigureouttherecursionformulaandasymptoticformulaoftheLaurentcoe佑cients：Inchapter4，westudytheproperholomorphicmappingsonboundedsimplyconnecteddoma

7、insInthischapter，byliftingsimplyconnecteddomainontounitdisc，weobtaintheequalityrelationshipbetweenthecomponentnumbersoftheboundarypointoftherangeanditsdifferentinverseimagepointswealsodiscusstheinequalityrelationshipbetw

8、eenthetopologicaldegreeoftheproperholomorphicmappingandthenumbersofthedifferentinverseimagepointsbasedontheboundarypointiSacutpointornotKeywords：CBB，3levelSierpinskinumber，Propermappinggasket，Cauchytransform，ComponentIII