偏微分方程（第2卷）（第2版）
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作者[美]泰勒（M．E．Taylor） 著
出版社世界图书出版公司
出版时间2014-01
版次2
装帧平装
上书时间2024-12-03
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图书标准信息
- 作者 [美]泰勒（M．E．Taylor） 著
- 出版社 世界图书出版公司
- 出版时间 2014-01
- 版次 2
- ISBN 9787510068140
- 定价 99.00元
- 装帧 平装
- 开本 24开
- 纸张 胶版纸
- 页数 614页
- 正文语种 英语
- 【内容简介】
- ThisworkisintendedtoprovideacourseofstudyofsomeofthemajoraspectsofPDE.ItisaddressedtoreaderswithabackgroundinthebasicintroductorygraduatemathematicscoursesinAmericanuniversities:elementaryrealandcomplexanalysis，differentialgeometry，andmeasuretheory.
- 【目录】
-
ContentsofVolumesIandIII
Preface
7PseudodifferentialOperators
1TheFourierintegralrepresentationandsymbolclasses
2Schwartzkernelsofpseudodifferentialoperators
3Adjointsandproducts
4Ellipticoperatorsandparametrices
5L2estimates
6Garding'sinequality
7Hyperbolicevolutionequations.
8Egorov'stheorem
9Microlocalregularity
10Operatorsonmanifolds
11Themethodoflayerpotentials
12Parametrixforregularellipticboundaryproblems
13Parametrixfortheheatequation
14TheWeylcalculus
15Operatorsofharmonicoscillatortype
Reference
8SpectralTheory
1Thespectraltheorem
2Self-adjointdifferentialoperators
3Heatasymptoticsandeigenvalueasymptotics
4TheLaplaceoperatoronSn
5TheLaplaceoperatoronhyperbolicspace
6Theharmonicoscillator
7ThequantumCoulombproblem
8TheLaplaceoperatoroncones
References
9ScatteringbyObstacles
1Thescatteringproblem
2Eigenfunctionexpansions
3Thescatteringoperator
4Connectionswiththewaveequatio
5Waveoperators
6TranslationrepresentationsandtheLax-PhillipssemigroupZ（t）
7Integralequationsandscatteringpoles
8Traceformulas;thescatteringphase
9Scatteringbyasphere
10Inverseproblemsl
11InverseproblemsII
12Scatteringbyroughobstacles
ALidskii'stracetheorem
References
10DiracOperatorsandIndexTheory
1OperatorsofDiractype
2Cliffordalgebras
3Spinors
4Weitzenbockformulas
5IndexofDiracoperators
6Proofofthelocalindexformula
7TheChern-Gauss-Bonnettheorem
8Spincmanifolds
9TheRiemann-Rochtheorem
10Directattackin2-D
11Indexofoperatorsofharmonicoscillatortype
References
11BrownianMotionandPotentialTheory
1BrownianmotionandWienermeasure
2TheFeynman-Kacformula
3TheDirichletproblemanddiffusionondomainswithboundary
4Martingales,stoppingtimes,andthestrongMarkovproperty
5FirstexittimeandthePoissonintegral
6Newtoniancapacity
7Stochasticintegrals
8Stochasticintegrals,II
9Stochasticdifferentialequations
10Applicationtoequationsofdiffusio
ATheTrotterproductformula
References
……
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