调和分析基础教程

图书标准信息

• 作者 [英]特玛 著
• 出版社 世界图书出版公司
• 出版时间 2009-06
• 版次 1
• ISBN 9787510004827
• 定价 25.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 192页
• 正文语种 英语

【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