Clifford分析中無(wú)界域上幾類正則函數(shù)的Cauchy積分公式及邊值問(wèn)題.pdf

1、寧夏大學(xué)碩士學(xué)位論文Cliffd分析中無(wú)界域上幾類正則函數(shù)的Cauchy積分公式及邊值問(wèn)題姓名：楊紅霞申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：韓惠麗20090301寧夏大學(xué)碩十學(xué)位論文英文摘要AbstractCliffordanalysisoffersafunctiontheoryforthesolutionofDiracequationforspinorfieldandisassuchadirectgenerationtohighe

2、rdimensionsoftheclassicalfunctiontheoryofholomorphicfunctioninthecomplexplaneThefunctionstaketheirvaluesinCliffordalgebra如，whichWassetupatthebeginningofthelastcenturyagradenoncommutativeandassociativealgebra，inwhicharbit

3、rarydimensionalrealorcomplexEuclideanspacemaybeembeddedinanaturalwayNotonlyfromthetheoreticalpointofviewbutalsowithrespecttoapplications，inparticulartobothelasticmechanicsandfluidmechanics，suchasMaxwellequation，theoryofY

4、angMillsfield，quantummechanicsandSOon，CliffordanalysishasproventobeavaluablecounterparttothetheoryofseveralcomplexvariablesNowadays，Cliffordanalysishasdevelopedintoanautonomousdisciplineinmathematicalanalysiswithresearch

5、groupsaUovertheworldManyscholarshavepaidmuchaHentiononitCauchyintegralformulasandtheboundaryvalueproblemoftypesofregularfunctionsonunboundeddomainsintheanalysisofCliffordarediscussedinthepaperThepaperCanbedividedintothre

6、echaptersasfollows：ThebackgroundknowledgeandthedevelopmentofCliffordalgebraaregiveninchapteroneThenthebasictheriticallyknowledgeofCliffordalgebraisalsogivenasnecessaryknowledgeforthefollowingchaptersCauchyintegralformula

7、sofsomecommonkindsofregularfunctiononboundeddomainsintheanalysisofCliffordareproposedfirstlyatthebeginningofchaptertwoTheCauchyintegralformulasandanotherkindofCauchyintegralformulaofhypermonogenicfunction(doubledhypermon

8、ogenicfunction)OilunboundeddomainsareobtainedbytheCauchyintegralformulaofregularfunctiononunboundeddomainsproposedbyJohnRanLinearyboundaryvalueproblemofregularfunctionvectorandhypermonogenicfunctiononunboundeddomainsasdi

9、scussedbasedontheamendedCauchykernelintheanalysisofCliffordisconsideredinchapterthree口(芒)垂@)6(芒)研c(芒)圣一(t)d(芒)研=g(t)fFortheboundaryvalueproblem，theplemeljformulasofregularfunctionvectorandhypermonogenicfunctiononunbounde

10、ddomainsaregivenThentheexistenceandunipuenessofthesolutionofthisprob—lemaredomenstratedbyintegralequationandCompressionfixedpointtheoremKeyWords：Cliffordanalysis，RegularfunctionvectorHypermonogenicfunction，Plemeljformula