扩散过程和偏微分方程：英文版

Preface
Acknowledgments
NotationandConventions
IatroduetionandSummary
IMarkovProcessesandSemigroups
IIPropagationofMaximums
IIIConstructionofFellerSemigroups
Chapter1PreparatoryMaterial
1.1Sets
1.2Mappings
1.3TopologicalSpaces
1.4Compactness
1.5Connectedness
1.6MetricSpaces
1.7Baire'sCategoryTheorem
1.8ContinuousMappings
1.9LinearSpaces
1.10LinearTopologicalSpaces
1.11FactorSpaces
1.12AlgebrasandModules
1.13LinearOperators
1.14DifferentiableMappings
1.15VectorFieldsandIntegralCurves
1.16MeasurableSpaces
1.17MeasurableFunctions
1.18Measures
1.19Integrals
1.20ProbabilitySpaces
Notes
Chapter2Manifolds,TensorsandDensities
2.1Manifolds
2.2CMappings
2.3TangentBundles
2.4VectorFields
2.5IntegralCurves
2.6CotangentBundles
2.7Tensors
2.8TensorFields
2.9ExteriorProduct
2.10DifferentialForms
2.11Densities
2.12IntegrationonManifolds
2.13ManifoldswithBoundary
Notes
Chapter3FunctionalAnalysis
3.1QuasinormedLinearSpaces
3.2NormedLinearSpaces
3.3TheRieszRepresentationTheorem
3.4ClosedOperators
3.5ComplementedSubspaces
3.6CompactOperators
3.7FredholmOperators
3.8HilbertSpaces
3.9TheoryofSemigroups
Notes
Chapter4Distributions,OperatorsandKernels
4.1Notation
4.2FunctionSpaces
4.3DifferentialOperators
4.4Distributions
4.5OperatorsandKernels
4.6DistributionsonaManifold
4.7DifferentialOperatorsonaManifold
4.8OperatorsandKernelsonaManifold
4.9DomainsofClassCr
4.10TheSee]eyExtensionTheorem
Notes
Chapter5SobolevSpaces
5.1TheSpacesHs(Rn)
5.2TheSpacesHsloc(Ω)
5.3TheSpacesHs(M)
5.4TheSpacesHs(Rn+)
5.5TheSpacesHs(Ω)
5.6TraceTheorems
5.7SobolevSpacesandRegularizations
Notes
Chapter6TheCalculusofPseudo-DifferentialOperators
6.1SymbolClasses
6.2PhaseFunctions
6.3OscillatoryIntegrals
6.4FourierIntegralOperators
6.5Pseudo-DifferentialOperators
6.6Pseudo-DifferentialOperatorsonaManifold
6.7EllipticPseudo-DifferentialOperatorsandtheirIndices
6.8PotentialsandPseudo-DifferentialOperators
6.9TheSharpGardingInequality
6.10HypoellipticPseudo-DifferentialOperators
Notes
Chapter7MaximumPrinciplesforDegenerateEllipticOperators
7.1MaximumPrinciples
7.2PropagationofMaximums
Notes
Chapter8EllipticBoundaryValueProblems
8.1TheDirichletProblem--(1)--
8.2TheDirichletProblem--(2)--
8.3GeneralBoundaryValueProblems
8.4ExistenceandUniquenessTheoremforGeneralBoundary
ValueProblems
Notes
Chapter9MarkovProcesses,SemigroupsandBoundaryValue
Problems
9.1MarkovProcessesandTransitionFunctions
9.2TransitionFunctionsandFellerSemigroups
9.3FellerSemigroupsandtheirInfinitesimalGenerators
9.4InfinitesimalGeneratorsofFellerSemigroups--(1)--
9.5InfinitesimalGeneratorsofFellerSemigroups--(2)--
9.6FellerSemigroupsandBoundaryValueProblems
Notes
Chapter10ConstructionofFellerSemigroups
10.1StatementofResults
10.2ProofofTheorem10.1.1
10.3ProofofTheorem10.1.3
Notes
Bibliography
ListofSymbols
Index