馆藏图书经典分析中的傅立叶积分
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九五品
仅1件
作者G.D.Sogge 编
出版社世界图书出版公司
出版时间2003-04
版次1
装帧平装
上书时间2024-08-12
商品详情
- 品相描述:九五品
图书标准信息
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作者
G.D.Sogge 编
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出版社
世界图书出版公司
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出版时间
2003-04
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版次
1
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ISBN
9787506259187
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定价
60.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
236页
- 【内容简介】
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Exceptforminormodifications,thismonographrepresentsthelecturenotesofacourseIgaveatUCLAduringthewinterandspringquartersof1991.MypurposeinthecoursewastopresentthenecessarybackgroundmaterialandtoshowhowideasfromthetheoryofFourierintegraloperatorscanbeusefulforstudyingbasictopicsinclassicalanalysis,suchasoscillatoryintegralsandmaximalfunctions.ThelinkbetweenthetheoryofFourierintegraloperatorsandclassicalanalysisisofcoursenotnew,sinceoneoftheearlygoalsofmicrolocalanalysiswastoprovidevariablecoefficientversionsoftheFouriertransform.However,theprimarygoalofthissubjectwastodeveloptoolsforthestudyofpartialdifferentialequationsand,tosomeextent,onlyrecentlyhavemanyclassicalanalystsrealizeditsutilityintheirsubject.
- 【目录】
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Preface
0.Background
0.1.FourierTransform
0.2.BasicRealVariableTheory
0.3.FractionalIntegrationandSobolevEmbeddingTheorems
0.4.WaveFrontSetsandtheCotangentBundle
0.5.OscillatoryIntegrals
Notes
1.StationaryPhase
1.1.StationaryPhaseEstimates
1.2.FourierTransformofSurface-carriedMeasures
Notes
2.Non-homogeneousOscillatoryIntegralOperators
2.1.Non-degenerateOscillatoryIntegralOperators
2.2.OscillatoryIntegralOperatorsRelatedtotheRestrictionTheorem
2.3.RieszMeansinR"
2.4.KakeyaMaximalFunctionsandMaximalRieszMeansinR2Notes
3.Pseudo-differentialOperators
3.1.SomeBasics
3.2.EquivalenceofPhaseFunctions
3.3.Self-adjointEllipticPseudo-differentialOperatorsonCompactManifoldsNotes
4.TheHalf-waveOperatorandFunctionsofPseudo-differentialOperators
4.1.TheHalf-waveOperator
4.2.TheSharpWeylFormula
4.3.SmoothFunctionsofPseudo-differentialOperatorsNotes
5.LPEstimatesofEigenfunctions
5.1.TheDiscreteL2RestrictionTheorem
5.2.EstimatesforRieszMeans
5.3.MoreGeneralMultiplierTheoremsNotes
6.FourierIntegralOperators
6.1.LagrangianDistributions
6.2.RegularityProperties
6.3.SphericalMaximalTheorems:Take1
Notes
7.LocalSmoothingofFourierIntegralOperators
7.1.LocalSmoothinginTwoDimensionsandVariableCoefficientKakeyaMaximalTheorems
7.2.LocalSmoothinginHigherDimensions
7.3.SphericalMaximalTheoremsRevisited
Notes
Appendix:LagrangianSubspacesofT*IRn
Bibliography
Index
IndexofNotation
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