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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

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