EMS__Several_Complex_Variables_02 .pdf

《EMS__Several_Complex_Variables_02 .pdf》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、G.M.KhenkinA.G.Vitushkin(Eds.)^2.SeveralComplexVariablesIIFunctionTheoryinClassicalDomainsComplexPotentialTheoryWith19FiguresSpringer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestEncyclopaediaofMathematicalSciencesVolume8Editor-in-Chief:R.VGamkrelidzeContentsI.M

2、ultidimensionalResiduesandApplicationsL.A.Aizenberg,A.K.Tsikh,A.P.Yuzhakov1II.PlurisubharmonicFunctionsA.Sadullaev59III.FunctionTheoryintheBallA.B.Aleksandrov107IV.ComplexAnalysisintheFutureTubeA.G.Sergeev,V.S.Vladimirov179AuthorIndex255SubjectIndex258I.MultidimensionalResiduesandApplic

3、ationsL.A.Aizenberg,A.K.Tsikh,A.P.YuzhakovTranslatedfromtheRussianbyJ.R.KingContentsChapter1.MethodsforComputingMultidimensionalResidues(A.P.Yuzhakov)3Introduction3§1.LerayTheory.FroissartDecompositionTheorem41.1.LerayCoboundary41.2.Form-Residue,Class-Residue,LerayResidueFormula51.3.Tes

4、tsforLerayCoboundaries.FroissartDecompositionTheorem61.4.CohomologicalLoweringofPoleOrder71.5.GeneralizationoftheLerayTheorytotheCaseofSubmanifoldsofCodimensionq>l9§2.ApplicationofAlexander-PontryaginDualityandDeRhamDuality102.1.ApplicationofAlexander-PontryaginDuality102.2.ResiduesofRa

5、tionalFunctionsofTwoVariables112.3.ApplicationofDeRhamDuality13§3.HomologicalMethodsforStudyingIntegralsthatDependuponParameters.ApplicationtoCombinatorialAnalysis153.1.AnalyticContinuationofIntegralsDependingonParameters.IsotopyTheorem163.2.FoliationnearaLandauSingularity.Picard-Lefsch

6、etzFormula183.3.SomeExamplesofIntegralsDependingonParameters203.4.ApplicationofResiduestoCombinatorialAnalysis22Chapter2.MultidimensionalLogarithmicResiduesandTheirApplications(L.A.Aizenberg)24§1.MultidimensionalLogarithmicResidues24§2.SeriesExpansionofImplicitFunctions312L.A.Aizenberg,

7、A.K.Tsikh,A.P.Yuzhakov§3.ApplicationoftheMultidimensionalLogarithmicResiduetoSystemsofNonlinearEquations33§4.ComputationoftheZero-MultiplicityofaHolomorphicMapping.37§5.ApplicationoftheMultidimensionalLogarithmicResiduetotheTheoryofNumbers38Chapter3.TheGrothendieckResidueandits