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ID:34860777
大小:1.31 MB
页数:268页
时间:2019-03-12
《Springer.Alexander.H.Wermer.J.Several.Complex.Variables.and.Banach.Algebras.(ISBN.0387982531)(3ed.Springer.1998)(268s)_MCf_》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、SeveralComplexVariablesandBanachAlgebras,ThirdEditionHerbertAlexanderJohnWermerSpringertoSusanandtothememoryofKerstinThispageintentionallyleftblankTableofContentsPrefacetotheSecondEditionixPrefacetotheRevisedEditionxiChapter1PreliminariesandNotation1Chapter2ClassicalApproxim
2、ationTheorems5Chapter3OperationalCalculusinOneVariable17Chapter4DifferentialForms23Chapter5The∂-Operator27Chapter6TheEquation∂uf31Chapter7TheOka-WeilTheorem36Chapter8OperationalCalculusinSeveralVariables43Chapter9TheSilovBoundaryˇ50Chapter10MaximalityandRado’sTheorem´57Chap
3、ter11MaximumModulusAlgebras64Chapter12HullsofCurvesandArcs84Chapter13IntegralKernels92Chapter14PerturbationsoftheStone–WeierstrassTheorem102Chapter15TheFirstCohomologyGroupofaMaximalIdealSpace112Chapter16The∂-OperatorinSmoothlyBoundedDomains120viiviiiTableofContentsChapter17
4、ManifoldsWithoutComplexTangents134Chapter18SubmanifoldsofHighDimension146Chapter19BoundariesofAnalyticVarieties155Chapter20PolynomialHullsofSetsOvertheCircle170Chapter21Areas180Chapter22TopologyofHulls187Chapter23PseudoconvexsetsinCn194Chapter24Examples206Chapter25Historical
5、CommentsandRecentDevelopments224Chapter26Appendix231Chapter27SolutionstoSomeExercises237Bibliography241Index251PrefacetotheSecondEditionDuringthepasttwentyyearsmanyconnectionshavebeenfoundbetweenthetheoryofanalyticfunctionsofoneormorecomplexvariablesandthestudyofcommutativeB
6、anachalgebras.Ontheonehand,functiontheoryhasbeenusedtoansweralgebraicquestionssuchasthequestionoftheexistenceofidempotentsinaBanachalgebra.Ontheotherhand,conceptsarisingfromthestudyofBanachalgebrassuchasthemaximalidealspace,theSilovboundary,Gleasonparts,etc.ˇhaveledtonewques
7、tionsandtonewmethodsofproofinfunctiontheory.Roughlyonethirdofthisbookisconcernedwithdevelopingsomeoftheprinci-palapplicationsoffunctiontheoryinseveralcomplexvariablestoBanachalgebras.Wepresupposenoknowledgeofseveralcomplexvariablesonthepartofthereaderbutdevelopthenecessaryma
8、terialfromscratch.Theremainderofthebookdealswithproblemsofuniformapproximat
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