数学研究生教材：半群上的调和分析（英文版）（影印版）

图书标准信息

• 作者 [丹]博格（Berg.G） 著
• 出版社 世界图书出版公司
• 出版时间 2012-08
• 版次 1
• ISBN 9787510047176
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 289页
• 正文语种 英语

【内容简介】

Thepurposeofthisbookistoprovideatreatmentofthesepositivedefinitefunctionsonabeliansemigroupswithinvolution.Indoingsowealsodiscussrelatedtopicssuchasnegativedefinitefunctions，completelymonotonefunctionsandHoeffding-typeinequalities.Weviewthesesubjectsasimportantingredientsofharmonicanalysisonsemigroups.Ithasbeenouraim，simultaneously，towriteabookwhichcanserveasatextbookforanadvancedgraduatecourse，becausewefeelthatthenotionofpositivedefinitenessisanimportantandbasicnotionwhichoccursinmathematicsasoftenasthenotionofaHilbertspace.ThealreadymentionedLaplaceandouriertransformations，aswellasthegeneratingfunctionsforintegervaluedrandomvariables，belongtothemostimportantanalyticaltoolsinprobabilitytheoryanditsapplications.Onlyrecentlyitturnedoutthatpositive（resp.negative）definitefunctionsallowaprobabilisticcharacterizationintermsofso-calledHoeffding-typeinequalities.

【目录】

CHAPTER1IntroductiontoLocallyConvexTopologicalVectorSpacesandDualPairs
1.LocallyConvexVectorSpaces
2.Hahn-BanachTheorems
3.DualPairs
NotesandRemarks

CHAPTER2RadonMeasuresandIntegralRepresentations
1.IntroductiontoRadonMeasuresonHausdorffSpaces
2.TheRieszRepresentationTheorem
3.WeakConvergenceofFiniteRadonMeasures
4.VagueConvergenceofRadonMeasuresonLocallyCompactSpaces
5.IntroductiontotheTheoryoflntegralRepresentations
NotesandRemarks

CHAPTER3GeneralResultsonPositiveandNegativeDefiniteMatricesandKernels
1.DefinitionsandSomeSimplePropertiesofPositiveandNegativeDefiniteKernels
2.RelationsBetweenPositiveandNegativeDefiniteKernels
3.HilbertSpaceRepresentationofPositiveandNegativeDefiniteKernels
NotesandRemarks

CHAPTER4MainResultsonPositiveandNegativeDefiniteFunctionsonSemigroups
1.DefinitionsandSimpleProperties
2.ExponentiallyBoundedPositiveDefiniteFunctionsonAbelianSemigroups
3.NegativeDefiniteFunctionsonAbelianSemigroups
4.ExamplesofPositiveandNegativeDefniteFunctions
5.PositiveFunctions
6.CompletelyMonotoneandAlternatingFunctions
NotesandRemarks

CHAPTER5Schoenberg-TypeResultsforPositiveandNegativeDefiniteFunctions
1.SchoenbergTriples
2.NormDependentPositiveDefiniteFunctionsonBanachSpaces
3.FunctionsOperatingonPositiveDefiniteMatrices
4.Schoenberg'sTheoremfortheComplexHilbertSphere
5.TheRealInfiniteDimensionalHypcrbolicSpace
NotesandRemarks

CHAPTER6PositiveDefiniteFunctionsandMomentFunctions
1.MomentFunctions
2.TheOne-DimensionalMomentProblem
3.TheMultiDimensionalMomentProblem
4.TheTwo-SidedMomentProblem
5.PerfectSemigroups
NotesandRemarks

CHAPTER7Hoeffding'sInequalityandMultivariateMajorization
1.TheDiscreteCase
2.ExtensiontoNondiscreteSemigroups
3.CompletelyNegativeDefiniteFunctionsandSchur-MonotonicityNotesandRemarks

CHAPTER8PositiveandNegativeDefiniteFunctionsonAbelianSemigroupsWithoutZero
1.QuasiboundedPositiveandNegativeDefiniteFunctions
2.CompletelyMonotoneandCompletelyAlternatingFunctions
NotesandRemarks
References
ListofSymbols
Index