国外数学名著系列·陶伯理论：百年进展（影印版）

图书标准信息

• 作者 [荷]科雷瓦 著
• 出版社 科学出版社
• 出版时间 2007-01
• 版次 1
• ISBN 9787030183033
• 定价 80.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 483页
• 字数 594千字
• 正文语种 英语
• 丛书 国外数学名著系列（影印版）

【内容简介】

《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】

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