EMS__Several_Complex_Variables_02 .pdf

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1、G.M.KhenkinA.G.Vitushkin(Eds.)^2.SeveralComplexVariablesIIFunctionTheoryinClassicalDomainsComplexPotentialTheoryWith19FiguresSpringer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestEncyclopaediaofMathematicalSciencesVolume8Edito

2、r-in-Chief:R.VGamkrelidzeContentsI.MultidimensionalResiduesandApplicationsL.A.Aizenberg,A.K.Tsikh,A.P.Yuzhakov1II.PlurisubharmonicFunctionsA.Sadullaev59III.FunctionTheoryintheBallA.B.Aleksandrov107IV.ComplexAnalysisintheFutureTubeA.G.Sergeev,V.S.Vladi

3、mirov179AuthorIndex255SubjectIndex258I.MultidimensionalResiduesandApplicationsL.A.Aizenberg,A.K.Tsikh,A.P.YuzhakovTranslatedfromtheRussianbyJ.R.KingContentsChapter1.MethodsforComputingMultidimensionalResidues(A.P.Yuzhakov)3Introduction3§1.LerayTheory.

4、FroissartDecompositionTheorem41.1.LerayCoboundary41.2.Form-Residue,Class-Residue,LerayResidueFormula51.3.TestsforLerayCoboundaries.FroissartDecompositionTheorem61.4.CohomologicalLoweringofPoleOrder71.5.GeneralizationoftheLerayTheorytotheCaseofSubmanif

5、oldsofCodimensionq>l9§2.ApplicationofAlexander-PontryaginDualityandDeRhamDuality102.1.ApplicationofAlexander-PontryaginDuality102.2.ResiduesofRationalFunctionsofTwoVariables112.3.ApplicationofDeRhamDuality13§3.HomologicalMethodsforStudyingIntegralstha

6、tDependuponParameters.ApplicationtoCombinatorialAnalysis153.1.AnalyticContinuationofIntegralsDependingonParameters.IsotopyTheorem163.2.FoliationnearaLandauSingularity.Picard-LefschetzFormula183.3.SomeExamplesofIntegralsDependingonParameters203.4.Appli

7、cationofResiduestoCombinatorialAnalysis22Chapter2.MultidimensionalLogarithmicResiduesandTheirApplications(L.A.Aizenberg)24§1.MultidimensionalLogarithmicResidues24§2.SeriesExpansionofImplicitFunctions312L.A.Aizenberg,A.K.Tsikh,A.P.Yuzhakov§3.Applicatio

8、noftheMultidimensionalLogarithmicResiduetoSystemsofNonlinearEquations33§4.ComputationoftheZero-MultiplicityofaHolomorphicMapping.37§5.ApplicationoftheMultidimensionalLogarithmicResiduetotheTheoryofNumbers38Chapter3.TheGrothendieckResidueandits