调和分析基础教程

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

　　本书由世界图书出版公司出版，主要内容包括：Exponentials、TheBesselInequality、ConvergenceintheL2-Norm、UniformConvergenceofFourierSeries、PeriodicFunctionsRevisited、Exercises等。