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《the convenient setting of global analysis》由會員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫。
1、MathematicalSurveysandMonographsVolume53TheConvenientSettingofGlobalAnalysisAndreasKrieglPeterW.MichorATHEMATICMALNTRHTOSMHEISITWSAOICCIREAmericanMathematicalSocietyEAGEWMETMYAF8O8UNDED18EditorialBoardHowardA.MasurMichaelRenardyTudorStefanRatiu,Chair1991MathematicsSubjectClassi?cation.Primary22E
2、65,26E15,26E20,46A17,46G05,46G20,46E25,46E50,58B10,58B12,58B20,58B25,58C20,46E50,58D05,58D10,58D15,58D17,58D19,58F25;Secondary22E45,58C40,22E67,46A16,57N20,58B05,58D07,58D25,58D27,58F05,58F06,58F07.Abstract.Theaimofthisbookistolayfoundationsofdi?erentialcalculusinin?nitedimensionsandtodiscusstho
3、seapplicationsinin?nitedimensionaldi?erentialgeometryandglobalanalysiswhichdonotinvolveSobolevcompletionsand?xedpointtheory.Theapproachisverysimple:Amappingiscalledsmoothifitmapssmoothcurvestosmoothcurves.Allotherpropertiesareprovedresultsandnotassumptions:Likechainrule,existenceandlinearityofde
4、rivatives,powerfulsmoothuniformlyboundednesstheoremsareavailable.UptoFr′echetspacesthisnotionofsmoothnesscoincideswithallknownreasonableconcepts.Inthesamespiritcalculusofholo-morphicmappings(includingHartogs’theoremandholomorphicuniformboundednesstheorems)andcalculusofrealanalyticmappingsaredeve
5、loped.Existenceofsmoothpartitionsofunity,thefoundationsofmanifoldtheoryinin?nitedimensions,therelationbetweentangentvectorsandderivations,anddi?erentialformsarediscussedthoroughly.Specialemphasisisgiventothenotionofregularin?nitedimensionalLiegroups.Manyapplicationsofthistheoryareincluded:manifo
6、ldsofsmoothmappings,groupsofdi?eomorphisms,geodesicsonspacesofRiemannianmetrics,directlimitmanifolds,perturbationtheoryofoperators,anddi?erentiabilityquestionsofin?nitedimensionalrepresentations.CorrectionsandcomplementstothisbookwillbepostedontheinternetattheURLhttp://www.mat.univie.ac.at/~mich
7、or/apbook.psLibraryofCongressCataloging-in-PublicationDataKriegl,Andreas.Theconvenientsettingofglobalanalysis/AndreasKriegl,PeterW.Michor.p.cm.—(Mathematicalsurveysandmonographs,ISSN0076-5376;v.53)Includesbibliographicalrefe
