数域上的傅里叶分析

图书标准信息

• 作者 罗摩克里希纳（DinakarRamakrishnan） 著
• 出版社 世界图书出版公司
• 出版时间 2011-07
• 版次 1
• ISBN 9787510037511
• 定价 45.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 350页
• 字数 263千字
• 正文语种 英语

【内容简介】

ThisbookgrewoutofnotesfromseveralcoursesthatthefirstauthorhastaughtoverthepastnineyearsattheCaliforniaInstituteofTechnology,andearlierattheJohnsHopkinsUniversity,CornellUniversity,theUniversityofChicago,andtheUniversityofCrete.Ourgeneralaimistoprovideamodernapproachtonumbertheorythroughablendingofcomplementaryalgebraicandanalyticperspectives,emphasizingharmonicanalysisontopologicalgroups.OurmoreparticulargoalistocoverJohnTate'svisionarythesis,givingvirtuallyallofthenecessaryanalyticdetailsandtopologicalpreliminaries——technicalprereq-uisitesthatareoftenforeigntothetypical,morealgebraicallyinclinednumbertheorist.MostoftheexistingtreatmentsofTate'sthesis,includingTate'sown,rangefromtersetocryptic;ourintentistobemoreleisurely,morecomprehen-sive,andmorecomprehensible.Tothisendwehaveassembledmaterialthathasadmittedlybeentreatedelsewhere,butnotinasinglevolumewithsomuchdetailandnotwithourparticularfocus.

【目录】

PREFACE
INDEXOFNOTATION
TOPOLOGICALGROUPS
1.1BasicNotions
1.2HaarMeasure
1.3ProfiniteGroups
1.4Pro-p-Groups
Exercises

2SOMEREPRESENTATIONTHEORY
2.1RepresentationsofLocallyCompactGroups
2.2BanachAlgebrasandtheGelfandTransform
2.3TheSpectralTheorems
2.4UnitaryRepresentations
Exercises

3DUALITYFORLOCALLYCOMPACTABELIANGROUPS
3.1ThePontryaginDual
3.2FunctionsofPositiveType
3.3TheFourierInversionFormula
3.4PontryaginDuality
Exercises

4THESTRUCTUREOFARITHMETICFIELDS
4.ITheModuleofanAutomorphism
4.2TheClassificationofLocallyCompactFields
4.3ExtensionsofLocalFields
4.4PlacesandCompletionsofGlobalFields
4.5RamificationandBases
Exercises

5ADELES,IDELES,ANDTHECLASSGROUPS
5.1RestrictedDirectProducts,Characters,andMeasures
5.2Adeles,Ideles,andtheApproximationTheorem
5.3TheGeometryofAr/K
5.4TheClassGroups
Exercises

6AQUICKTOUROFCLASSFIELDTHEORY
6.1FrobeniusElements
6.2TheTchebotarevDensityTheorem
6.3TheTransferMap
6.4Artin'sReciprocityLaw
6.5AbelianExtensionsofQandQp
Exercises

7TATE'STHESISANDAPPLICATIONS
7.1Local（-Functions
7.2TheRiemann-RochTheorem
7.3TheGlobalFunctionalEquation
7.4HeckeL-Functions.
7.5TheVolumeofCandtheRegulator
7.6Dirichlet'sClassNumberFormula
7.7NonvanishingontheLineRe（s）——I
7.8ComparisonofHeckeL-Functions
Exercises

APPENDICES
AppendixA:NormedLinearSpaces
A.1Finite-DimensionalNormedLinearSpaces
A.2TheWeakTopology
A.3TheWeak-SlatTopology
A.4AReviewofLP-SpacesandDuality
AppendixB:DedekindDomains
B.1BasicProperties
B.2ExtensionsofDedekindDomains
REFERENCES
INDEX