国外数学名著系列·陶伯理论:百年进展(影印版)
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作者[荷]科雷瓦 著
出版社科学出版社
出版时间2007-01
版次1
装帧精装
货号6/2b4
上书时间2024-08-27
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图书标准信息
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作者
[荷]科雷瓦 著
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出版社
科学出版社
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出版时间
2007-01
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版次
1
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ISBN
9787030183033
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定价
80.00元
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装帧
精装
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开本
16开
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纸张
胶版纸
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页数
483页
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字数
594千字
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正文语种
英语
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丛书
国外数学名著系列(影印版)
- 【内容简介】
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《国外数学名著系列(影印版)36:陶伯理论百年进展》对收敛性、剩余估计等方面的知识作了全面的论述,作者按照自己对这些知识的独到的见解,用简便易懂的叙述方式诠释了那些非常难懂的定理性质等内容,叙述得可谓非常漂亮。陶伯理论对级数和积分的可求和性判定的不同方法加以比较,确定它们何时收敛,给出渐近估计和余项估计。由陶伯理论的最初起源开始,作者介绍该理论的发展历程:他的专业评论再现了早期结果所引来的兴奋;论及困难而令人着迷的哈代-李特尔伍德定理及其出人意料的一个简洁证明;高度赞扬维纳基于傅里叶理信论的突破,引人入胜的“高指数”定理以及应用于概率论的Karamata正则变分理论。作者也提及盖尔范德对维纳理论的代数处理以及基本人的分布方法。介绍了博雷尔方法和“圆”方法的一个统一的新理论,《国外数学名著系列(影印版)36:陶伯理论百年进展》还讨论研究素数定理的各种陶伯方法。书后附有大量参考文献和详细尽的索引。
- 【目录】
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ⅠTheHardy-LittlewoodTheorems
1Introduction
2ExamplesofSummabilityMethodsAbelianTheoremsandTauberianQuestion
3SimpleApplicationsofCesa()ro,AbelandBorelSummability
4LambertSummabilityinNumberTheory
5TaubersTheoremsforAbelSummability
6TauberianTheoremforCesa()roSummability
7Hardy-LittlewoodTauberiansforAbelSummability
8TauberiansInvolvingDirichletSeries
9TauberiansforBorelSummability
10LambertTauberianandPrimeNumberTheorem
11KaramatasMethodforPowerSeries
12WielandtsVariationontheMethod
13TransitionfromSeriestoIntegrals
14ExtensionofTaubersTheoremstoLaplace-StieltjesTransforms
15Hardy-LittlewoodTypeTheoremsInvolvingLaplaceTransforms
16OtherTauberianConditions:SlowlyDecreasingFunctions
17AsymptoticsforDerivatives
18IntegralTauberiansforCesa()roSummability
19TheMethodoftheMonotoneMinorant
20BoundednessTheoremInvolvingaGeneral-KernelTransform
21Laplace-StieltjesandStieltjesTransform
22GeneralDirichletSeries
23TheHigh-IndicesTheorem
24OptimalityofTauberianConditions
25TauberianTheoremsofNonstandardType
26ImportantPropertiesoftheZetaFunction
ⅡWienersTheory
1Introduction
2WienerProblem:PittsForm
3TestingEquationforWienerKernels
4OriginalWienerProblem
5WienersTheoremWithAdditionsbyPitt
6DirectApplicationsoftheTestingEquations
7FourierAnalysisofWienerKernels
8ThePrincipalWienerTheorems
9ProofoftheDivisionTheorem
10WienerFamiliesofKernels
11DistributionalApproachtoWienerTheory
12GeneralTauberianforLambertSummabilitY
13WienersSecondTauberianTheorem
14AWienerTheoremforSeries
15Extensions
16DiscussionoftheTauberianConditions
17Landau-InghamAsymptotics
18InghamSummability
19ApplicationofWienerTheorytoHarmonicFunctions
ⅢComplexTauberianTheorems
1Introduction
2ALandau-TypeTauberianforDirichletSeries
3MellinTransforms
4TheWiener-IkeharaTheorem
5NewerApproachtoWiener-Ikehara
6NewmansWaytothePNT.WorkofIngham
7LaplaceTransformsofBoundedFunctions
8ApplicationtoDirichletSeriesandthePNT
9LaplaceTransformsofFunctionsBoundedFromBelow
10TauberianConditionsOtherThanBoundedness
11AnOptimalConstantinTheorem10.1
12FatouandRiesz.GeneralDirichletSeries
13NewerExtensionsofFatou-Riesz
14PseudofunctionBoundaryBehavior
15ApplicationstoOperatorTheory
16ComplexRemainderTheory
17TheRemainderinFatousTheorem
18RemaindersinHardy-LittlewoodTheoremsInvolvingPowerSeries
19ARemainderfortheStieltjesTransform
ⅣKaramatasHeritage:RegularVariation
1Introduction
2SlowandRegularVariation
3ProofoftheBasicProperties
4PossiblePathology
5KaramatasCharacterizationofRegularly.VaryingFunctions
6RelatedClassesofFunctions
7IntegralTransformsandRegularVariation:Introduction
8KaramatasTheoremforLaplaceTransforms
9StieltjesandOtherTransforms
10TheRatioTheorem
11BeurlingSlowVariation
12AResultinHigher-OrderTheory
13MercerianTheorems
14ProofofTheorem13.2
15AsymptoticsInvolvingLargeLaplaceTransforms
16TransformsofExponentialGrowth:LogarithmicTheory
17StrongAsymptotics:GeneralCase
18ApplicationtoExponentialGrowth
19VeryLargeLaplaceTransforms
20LogarithmicTheoryforVeryLargeTransforms
21LargeTransforms:ComplexApproach
22ProofofProposition21.4
23AsymptoticsforPartitions
24Two-SidedLaplaceTransforms
ⅤExtensionsoftheClassicalTheory
1Introduction
2PreliminariesonBanachAlgebras
3AlgebraicFormofWienersTheorem
4WeightedL1Spaces
5GelfandsTheoryofMaximalIdeals
6ApplicationtotheBanachAlgebraAω=(Lω,C)
7RegularityConditionforLω
8TheClosedMaximalIdealsinLω
9RelatedQuestionsInvolvingWeightedSpaces
10ABoundednessTheoremofPitt
11ProofofTheorem10.2,Part1
12Theorem10.2:ProofthatS(y)=Q(eεY)
13Theorem10.2:ProofthatS(y)=Q{eφ(y)
14BoundednessThroughFunctionalAnalysis
15LimitableSequencesasElementsofanFK-space
16PerfectMatrixMethods
17MethodswithSectionalConvergence
18Existenceof(Limitable)BoundedDivergentSequences
19BoundedDivergentSequences,Continued
20GapTauberianTheorems
21TheAbelMethod
22RecurrentEvents
23TheTheoremofErd6s,FellerandPollard
24MilinsTheorem
25SomePropositions
26ProofofMilinsTheorem
ⅥBorelSummabilityandGeneralCircleMethods
1Introduction
2TheMethodsBandB
3BorelSummabilityofPowerSeries
4TheBorelPolygon
5GeneralCircleMethodsFλ
6AuxiliaryEstimates
7SerieswithOstrowskiGaps
8BoundednessResults
9IntegralFormulasforLimitability
10IntegralFormulas:CaseofPositiveSn
11FirstFormoftheTauberianTheorem
12GeneralTauberianTheoremwithSchmidtsCondition
13TauberianTheorem:CaseofPositiveSn
14AnApplicationtoNumberTheory
15High-IndicesTheorems
16RestrictedHigh-IndicesTheoremforGeneralCircleMethods
17TheBorelHigh-IndicesTheorem
18DiscussionoftheTauberianConditions
19GrowthofPowerSerieswithSquare-RootGaps
20EulerSummability
21TheTaylorMethodandOtherSpecialCircleMethods
22TheSpecialMethodsasFλ-Methods
23High-IndicesTheoremsforSpecialMethods
24PowerSeriesMethods
25ProofofTheorem24.4
ⅦTauberianRemainderTheory
1Introduction
2PowerSeriesandLaplaceTransforms:HowtheTheoryDeveloped
3TheoremsforLaplaceTransforms
4ProofofTheorems3.1and3.2
5One-SidedL1Approximation
6ProofofProposition5.2
7ApproximationofSmoothFunctions
8ProofofApproximationTheorem3.4
9VanishingRemainders:Theorem3.3
10OptimalityoftheRemainderEstimates
11DirichletSeriesandHighIndices
12ProofofTheorem11.2,Continued
13TheFourierIntegralMethod:Introduction
14FourierIntegralMethod:AModelTheorem
15AuxiliaryInequalityofGanelius
16ProofoftheModelTheorem
17AMoreGeneralTheorem
18ApplicationtoStieltjesTransforms
19FourierIntegralMethod:Laplace-StieltjesTransform
20RelatedResults
21NonlinearProblemsofErd6sforSequences
22IntroductiontotheProofofTheorem21.3
23ProofofTheorem21.3,Continued
24AnExampleandSomeRemarks
25IntroductiontotheProofofTheorem21.5
26TheFundamentalRelationandaReduction
27ProofofTheorem25.1,Continued
28TheEndGame
References
Index
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