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[美] 泰勒 (M.E.Taylor) 著 / 世界图书出版公司 / 2014-01 / 平装
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偏微分方程(第2卷)(第2版)
ThisworkisintendedtoprovideacourseofstudyofsomeofthemajoraspectsofPDE.ItisaddressedtoreaderswithabackgroundinthebasicintroductorygraduatemathematicscoursesinAmericanuniversities:elementaryrealandcomplexanalysis,differentialgeometry,andmeasuretheory.
ContentsofVolumesIandIIIPreface7PseudodifferentialOperators1TheFourierintegralrepresentationandsymbolclasses2Schwartzkernelsofpseudodifferentialoperators3Adjointsandproducts4Ellipticoperatorsandparametrices5L2estimates6Garding'sinequality7Hyperbolicevolutionequations.8Egorov'stheorem9Microlocalregularity10Operatorsonmanifolds11Themethodoflayerpotentials12Parametrixforregularellipticboundaryproblems13Parametrixfortheheatequation14TheWeylcalculus15OperatorsofharmonicoscillatortypeReference8SpectralTheory1Thespectraltheorem2Self-adjointdifferentialoperators3Heatasymptoticsandeigenvalueasymptotics4TheLaplaceoperatoronSn5TheLaplaceoperatoronhyperbolicspace6Theharmonicoscillator7ThequantumCoulombproblem8TheLaplaceoperatoronconesReferences9ScatteringbyObstacles1Thescatteringproblem2Eigenfunctionexpansions3Thescatteringoperator4Connectionswiththewaveequatio5Waveoperators6TranslationrepresentationsandtheLax-PhillipssemigroupZ(t)7Integralequationsandscatteringpoles8Traceformulas;thescatteringphase9Scatteringbyasphere10Inverseproblemsl11InverseproblemsII12ScatteringbyroughobstaclesALidskii'stracetheoremReferences10DiracOperatorsandIndexTheory1OperatorsofDiractype2Cliffordalgebras3Spinors4Weitzenbockformulas5IndexofDiracoperators6Proofofthelocalindexformula7TheChern-Gauss-Bonnettheorem8Spincmanifolds9TheRiemann-Rochtheorem10Directattackin2-D11IndexofoperatorsofharmonicoscillatortypeReferences11BrownianMotionandPotentialTheory1BrownianmotionandWienermeasure2TheFeynman-Kacformula3TheDirichletproblemanddiffusionondomainswithboundary4Martingales,stoppingtimes,andthestrongMarkovproperty5FirstexittimeandthePoissonintegral6Newtoniancapacity7Stochasticintegrals8Stochasticintegrals,II9Stochasticdifferentialequations10ApplicationtoequationsofdiffusioATheTrotterproductformulaReferences……
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