现代数学物理方法（第1、2、3、4卷）

图书标准信息

• 作者 M.Reed、B.Simon 编
• 出版社 世界图书出版公司
• 出版时间 2003-06
• 版次 1
• ISBN 9787506259316
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 400页

【内容简介】

Thisbookisthefirstofamultivolumeseriesdevotedtoanexpositionoffunctionalanalysismethodsinmodemmathematicalphysics.Itdescribesthefundamentalprinciplesoffunctionalanalysisandisessentiallyself-contained,althoughthereareoccasionalreferencestolatervolumes.Wehaveincludedafewapplicationswhenwethoughtthattheywouldprovidemotivationforthereader.Latervolumesdescribevariousadvancedtopicsinfunctionalanalysisandgivenumerousapplicationsinclassicalphysics,modemphysics,andpartialdifferenrialequations.

【目录】

Preface
Introduction
ContentsofOtherVolumes
I:PRELIMINARIES
1.Setsandfunctions
2.Metricandnormedlinearspaces
AppendixLirasupandliminf
3.TheLebesgueintegral
4.Abstractmeasuretheory
5.Twoconrergencearguments
6.Equicontinuity
Notes
Problems

II:HILBERTSPACES
1.ThegeometryofHilbertspace
2.TheRieszlemma
3.Orthonormalbases
4.TensorproductsofHilbertspaces
5.Ergodictheory:anintroduction
Notes
Problems

III:BANACHSPACES
1.Definitionandexamples
2.Dualsanddoubleduals
3.TheHahn-Banachtheorem
4.OperationsonBanachspaces
5.TheBairecategorytheoremanditsconsequences
Notes
Problems
IV:TOPOLOGICALSPACES
1.Generalnotions
2.NetsandConvergence
3.Compactness
AppendixTheStone-Weierstrasstheorem
4.MeasuretheoryonCompactspaces
5.WeaktopologiesonBanachspaces
AppendixWeakandstrongmeasurability
Notes
Problems

V:LOCALLYONVEXSPACES
1.Generalproperties
2.Frdchetspaces
3.Functionsofrapiddeceaseandthetempereddistributions
AppendixTheN-representationforand
4.Inductivelimits:generalizedfunctionsandweaksolutionsofpartialdifferentialequations
5.Fixedpointtheorems
6.Applicationsoffixedpointtheorems
7.Topologiesonlocallyconvexspaces:dualitytheoryandthestrongdualtopology
AppendixPolarsandtheMackey-Arenstheorem
Notes
Problems
VI:BOUNDEDOPERATORS
VII:THESPECTRALTHEOREM
VIII:UNBOUNDEDOPERATORS
THEFOURIERTRANSFORM
SUPPLEMENTARYMATERIAL
ListofSymbols