线性偏微分算子分析第1卷第2版(英文影印版)

线性偏微分算子分析第1卷第2版(英文影印版)

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作者: L.Hormander 著

出版社: 世界图书出版公司

出版时间: 2005-06

版次: 2

ISBN: 9787506272766

定价: 65.00

装帧: 平装

开本: 24开

纸张: 胶版纸

页数: 440页

正文语种: 英语

分类: 自然科学

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Theprogressinthetheoryoflinearpartialdifferentialequationsduringthepast30yearsowesmuchtothetheoryofdistributionscreatedbyLaurentSchwartzattheendofthe1940's.Itsummedupagreatdealoftheexperienceaccumulatedinthestudyofpartialdiffer-entialequationsuptothattime，andithasprovidedanidealframe-workforlaterdevelopments."Linearpartialdifferentialoperators"be-ganwithabriefsummaryofdistributiontheoryforthiswasstillun-familiartomanyanalysts20yearsago.Thepresentationthenpro-ceededdirectlytothemostgeneralresultsavailableonpartialdiffer-entialoperators.Thusthereaderwasexpectedtohavesomepriorfa-miliaritywiththeclassicaltheoryalthoughitwasnotappealedtoex-plicitly.Todayitmaynolongerbenecessarytoincludebasicdistribu-tiontheorybutitdoesnotseemreasonabletoassumeaclassicalbackgroundinthetheoryofpartialdifferentialequationssincemod-erntreatmentsarerare.Nowthetechniquesdevelopedinthestudyofsingularitiesofsolutionsofdifferentialequationsmakeitpossibletoregardafairamountofthismaterialasconsequencesofextensionsofdistri'outiontheory.RatherthanomittingdistributiontheoryIhavethereforedecidedtomakethefirstvolumeofthisbookagreatlyex-pandedtreatmentofit.Thetitlehasbeenmodifiedsothatitindicatesthegeneralanalyticalcontentsofthisvolume.
…… Introduction
ChapterⅠTestFunctions
Summary
1.1AreviewofDifferentialCalculus
1.2ExistenceofTestFunctions
1.3Convolution
1.4CutoffFunctionsandPartitionsofUnity
Notes

ChapterⅡDefinitionandBasicPropertiesofDistributions
Summary
2.1BasicDefinitions
2.2Localization
2.3DistributionswithCompactSupport
Notes

ChapterⅢDifferentiationandMultiplicationbyFunctions
Summary
3.1DefinitionandExamples
3.2HomogeneousDistributions
3.3SomeFundamentalSolutions
3.4EvaluationofSomeIntegrals
Notes

ChapterⅣConvolution
Summary
4.1ConvolutionwithaSmoothFunction
4.2ConvolutionofDistributions
4.3TheTheoremofSupports
4.4TheRoleofFundamentalSolutions
4.5BasicLpEstimatesforConvolutions
Notes

ChapterⅤDistributionsinProductSpaces
Summary
5.1TensorProducts
5.2TheKernelTheorem
Notes

ChapterⅥCompositionwithSmoothMaps
Summary
6.1Definitions
6.2SomeFundamentalSolutions
6.3DistributionsonaManifold
6.4TheTangentandCotangentBundles
Notes

ChapterⅦTheFourierTransformation
Summary
7.1TheFourierTransformationinandin
7.2PoissonsSummationFormulaandPeriodicDistributions
7.3TheFourier-LaplaceTransformationin
7.4MoreGeneralFourier-LaplaceTransforms
7.5TheMalgrangePreparatioTheorem
7.6FourierTransformsofGaussianFunctions
7.7TheMethodofStationaryPhase
7.8OscillatoryIntegrals
7.9H(s)LpandHolderEstimates
Notes

ChapterⅧSpectralAnalysisofSingularities
Summary
8.1TheWaveFrontSet
8.2AReviewofOperationswithDistributions
8.3TheWaveFrontSetofSolutionsOfPartialDifferentialEquations
8.4THeWaveFrontSetWithRespectto
8.5RulesofComputationforWFL
8.6WFLforSolutionsofPartialDifferentialEquations
8.7Microhyperbolicity
Notes

ChapterⅨHyperfunctions

Exercises
AnswersandHintstoAlltheExercises
Bibliography
Index
IndexofNotation
内容简介:
Theprogressinthetheoryoflinearpartialdifferentialequationsduringthepast30yearsowesmuchtothetheoryofdistributionscreatedbyLaurentSchwartzattheendofthe1940's.Itsummedupagreatdealoftheexperienceaccumulatedinthestudyofpartialdiffer-entialequationsuptothattime，andithasprovidedanidealframe-workforlaterdevelopments."Linearpartialdifferentialoperators"be-ganwithabriefsummaryofdistributiontheoryforthiswasstillun-familiartomanyanalysts20yearsago.Thepresentationthenpro-ceededdirectlytothemostgeneralresultsavailableonpartialdiffer-entialoperators.Thusthereaderwasexpectedtohavesomepriorfa-miliaritywiththeclassicaltheoryalthoughitwasnotappealedtoex-plicitly.Todayitmaynolongerbenecessarytoincludebasicdistribu-tiontheorybutitdoesnotseemreasonabletoassumeaclassicalbackgroundinthetheoryofpartialdifferentialequationssincemod-erntreatmentsarerare.Nowthetechniquesdevelopedinthestudyofsingularitiesofsolutionsofdifferentialequationsmakeitpossibletoregardafairamountofthismaterialasconsequencesofextensionsofdistri'outiontheory.RatherthanomittingdistributiontheoryIhavethereforedecidedtomakethefirstvolumeofthisbookagreatlyex-pandedtreatmentofit.Thetitlehasbeenmodifiedsothatitindicatesthegeneralanalyticalcontentsofthisvolume.
……
目录:
Introduction
ChapterⅠTestFunctions
Summary
1.1AreviewofDifferentialCalculus
1.2ExistenceofTestFunctions
1.3Convolution
1.4CutoffFunctionsandPartitionsofUnity
Notes

ChapterⅡDefinitionandBasicPropertiesofDistributions
Summary
2.1BasicDefinitions
2.2Localization
2.3DistributionswithCompactSupport
Notes

ChapterⅢDifferentiationandMultiplicationbyFunctions
Summary
3.1DefinitionandExamples
3.2HomogeneousDistributions
3.3SomeFundamentalSolutions
3.4EvaluationofSomeIntegrals
Notes

ChapterⅣConvolution
Summary
4.1ConvolutionwithaSmoothFunction
4.2ConvolutionofDistributions
4.3TheTheoremofSupports
4.4TheRoleofFundamentalSolutions
4.5BasicLpEstimatesforConvolutions
Notes

ChapterⅤDistributionsinProductSpaces
Summary
5.1TensorProducts
5.2TheKernelTheorem
Notes

ChapterⅥCompositionwithSmoothMaps
Summary
6.1Definitions
6.2SomeFundamentalSolutions
6.3DistributionsonaManifold
6.4TheTangentandCotangentBundles
Notes

ChapterⅦTheFourierTransformation
Summary
7.1TheFourierTransformationinandin
7.2PoissonsSummationFormulaandPeriodicDistributions
7.3TheFourier-LaplaceTransformationin
7.4MoreGeneralFourier-LaplaceTransforms
7.5TheMalgrangePreparatioTheorem
7.6FourierTransformsofGaussianFunctions
7.7TheMethodofStationaryPhase
7.8OscillatoryIntegrals
7.9H(s)LpandHolderEstimates
Notes

ChapterⅧSpectralAnalysisofSingularities
Summary
8.1TheWaveFrontSet
8.2AReviewofOperationswithDistributions
8.3TheWaveFrontSetofSolutionsOfPartialDifferentialEquations
8.4THeWaveFrontSetWithRespectto
8.5RulesofComputationforWFL
8.6WFLforSolutionsofPartialDifferentialEquations
8.7Microhyperbolicity
Notes

ChapterⅨHyperfunctions

Exercises
AnswersandHintstoAlltheExercises
Bibliography
Index
IndexofNotation

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