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alexander, wermer several complex variables and banach algebras gtm 35 (1998)外语英文电子书

alexander, wermer several complex variables and banach algebras gtm 35 (1998)外语英文电子书

ID：7884870

大小：1.53 MB

页数：268页

时间：2018-03-01

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1、SeveralComplexVariablesandBanachAlgebras,ThirdEditionHerbertAlexanderJohnWermerSpringertoSusanandtothememoryofKerstinThispageintentionallyleftblankTableofContentsPrefacetotheSecondEditionixPrefacetotheRevisedEditionxiChapter1PreliminariesandNotation1Chapter2ClassicalApproximatio

2、nTheorems5Chapter3OperationalCalculusinOneVariable17Chapter4DifferentialForms23Chapter5The∂-Operator27Chapter6TheEquation∂uf31Chapter7TheOka-WeilTheorem36Chapter8OperationalCalculusinSeveralVariables43Chapter9TheSilovBoundaryˇ50Chapter10MaximalityandRado’sTheorem´57Chapter11Max

3、imumModulusAlgebras64Chapter12HullsofCurvesandArcs84Chapter13IntegralKernels92Chapter14PerturbationsoftheStone–WeierstrassTheorem102Chapter15TheFirstCohomologyGroupofaMaximalIdealSpace112Chapter16The∂-OperatorinSmoothlyBoundedDomains120viiviiiTableofContentsChapter17ManifoldsWit

4、houtComplexTangents134Chapter18SubmanifoldsofHighDimension146Chapter19BoundariesofAnalyticVarieties155Chapter20PolynomialHullsofSetsOvertheCircle170Chapter21Areas180Chapter22TopologyofHulls187Chapter23PseudoconvexsetsinCn194Chapter24Examples206Chapter25HistoricalCommentsandRecen

5、tDevelopments224Chapter26Appendix231Chapter27SolutionstoSomeExercises237Bibliography241Index251PrefacetotheSecondEditionDuringthepasttwentyyearsmanyconnectionshavebeenfoundbetweenthetheoryofanalyticfunctionsofoneormorecomplexvariablesandthestudyofcommutativeBanachalgebras.Ontheo

6、nehand,functiontheoryhasbeenusedtoansweralgebraicquestionssuchasthequestionoftheexistenceofidempotentsinaBanachalgebra.Ontheotherhand,conceptsarisingfromthestudyofBanachalgebrassuchasthemaximalidealspace,theSilovboundary,Gleasonparts,etc.ˇhaveledtonewquestionsandtonewmethodsofpr

7、oofinfunctiontheory.Roughlyonethirdofthisbookisconcernedwithdevelopingsomeoftheprinci-palapplicationsoffunctiontheoryinseveralcomplexvariablestoBanachalgebras.Wepresupposenoknowledgeofseveralcomplexvariablesonthepartofthereaderbutdevelopthenecessarymaterialfromscratch.Theremaind

8、erofthebookdealswithproblemsofuniformapproximat

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