馆藏图书经典分析中的傅立叶积分

图书标准信息

• 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
• ISBN 9787506259187
• 定价 60.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 236页

【内容简介】

Exceptforminormodifications,thismonographrepresentsthelecturenotesofacourseIgaveatUCLAduringthewinterandspringquartersof1991.MypurposeinthecoursewastopresentthenecessarybackgroundmaterialandtoshowhowideasfromthetheoryofFourierintegraloperatorscanbeusefulforstudyingbasictopicsinclassicalanalysis,suchasoscillatoryintegralsandmaximalfunctions.ThelinkbetweenthetheoryofFourierintegraloperatorsandclassicalanalysisisofcoursenotnew,sinceoneoftheearlygoalsofmicrolocalanalysiswastoprovidevariablecoefficientversionsoftheFouriertransform.However,theprimarygoalofthissubjectwastodeveloptoolsforthestudyofpartialdifferentialequationsand,tosomeextent,onlyrecentlyhavemanyclassicalanalystsrealizeditsutilityintheirsubject.

【目录】

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