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Springer.Alexander.H.Wermer.J.Several.Complex.Variables.and.Banach.Algebras.(ISBN.0387982531)(3ed.Springer.1998)(268s)_MCf_

Springer.Alexander.H.Wermer.J.Several.Complex.Variables.and.Banach.Algebras.(ISBN.0387982531)(3ed.Springer.1998)(268s)_MCf_

ID：34860777

大小：1.31 MB

页数：268页

时间：2019-03-12

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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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