内容简介
Exponentials、TheBesselInequality、ConvergenceintheL2-Norm、UniformConvergenceofFourierSeries、PeriodicFunctionsRevisited、Exercises等。目录
IFourierAnalysis
1FourierSeries
1.1PeriodicFunctions
1.2Exponentials
1.3TheBesselInequality
1.4ConvergenceintheL2-Norm
1.5UniformConvergenceofFourierSeries
1.6PeriodicFunctionsRevisited
1.7Exercises
2HilbertSpaces
2.1Pre-HilbertandHilbertSpaces
2.22-Spaces
2.3OrthonormalBasesandCompletion
2.4FourierSeriesRevisited
2.5Exercises
3TheFourierTransform
3.1ConvergenceTheorems
3.2Convolution
3.3TheTransform
3.4TheInversionFormula
3.5PlancherelsTheorem
3.6ThePoissonSummationFormula
3.7ThetaSeries
3.8Exercises
4Distributions
4.1Definition
4.2TheDerivativeofaDistribution
4.3TemperedDistributions
4.4FourierTransform
4.5Exercises
IILCAGroups
5FiniteAbelianGroups
5.1TheDualGroup
5.2TheFourierTransform
5.3Convolution
5.4Exercises
6LCAGroups
6.1.MetricSpacesandTopology
6.2Completion
6.3LCAGroups
6.4Exercises
7TheDualGroup
7.1TheDualasLCAGroup
7.2PontryaginDuality
7.3Exercises
8PlancherelTheorem
8.1HaarIntegration
8.2FubinisTheorem
8.3Convolution
8.4PlancherelsTheorem
8.5Exercises
IIINoncommutativeGroups
9MatrixGroups
9.1GLn(C)andU(n)
9.2Representations
9.3TheExponential
9.4Exercises
10TheRepresentationsofSU(2)
10.1TheLieAlgebra
10.2TheRepresentations
10.3Exercises
11ThePeter-WeylTheorem
11.1DecompositionofRepresentations
11.2TheRepresentationonHom(Vr,VT)
11.3ThePeter-WeylTheorem
11.4AReformulation
11.5Exercises
12TheHeisenbergGroup
12.1Definition
12.2TheUnitaryDual
12.3Hilbert-SchmidtOperators
12.4ThePlancherelTheoremforH
12.5AReformulation
12.6Exercises
ATheRiemannZetaFunction
BHaarIntegration
Bibiliography
Index