希尔伯特空间及其空间导论（英文版）（第3版）

图书标准信息

• 作者 [美]德布纳斯（Debnath.L.） 著
• 出版社 世界图书出版公司
• 出版时间 2012-01
• 版次 1
• ISBN 9787510040665
• 定价 69.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 580页
• 正文语种 英语

【内容简介】

《希尔伯特空间及其空间导论（英文版）（第3版）》是一部学习希尔伯特空间的入门级教程。无论是学生还是科研人员，都将从本书的特别表达中受益。本书在原来版本的基础上做了不少改动，新增加了一部分讲述Sobolev空间，展开讲述了有限维赋范空间，有关小波的一章做了全面更新。并且包括了积分和微分方程、量子力学、最优化、变分和控制问题、逼近理论问题、非线性不稳定性和分岔理论的多种应用。在众多希尔伯特空间的书中，本书在讲述勒贝格积分方面独具特色。学习泛函分析和希尔伯特理论的老师和学生都十分推崇这本书作为教材或者参考书。

【目录】

prefacetothethirdedition
prefacetothesecondedition
prefacetothefirstedition
chapter1nermedvectorspaces
1.1introduction
1.2vectorspaces
1.3normedspaces
1.4knachspaces
1.slinearmappings
1.6contractionmappingsandthebanachfixedpointtheorem
1.7exercises

chapter2thelebesgueintegral
2.1introduction
2.2stepfunctions
2.3lebesl~eintelfablefunctions
2.4theabsolutevalueofoninteifablefunction
2.5seriesofintelqblefunctionsso
2.6norminl1（r）
2.7convergencealmosteverywheress
2.8fundamentolconvergencetheorems
2.9locallyintegmblefunctions
2.10thelebesgueintegralandtheriemannintegral
2.11lebesguemeasureonr
2.12complex-valuedlebesgueintegrablefunctions
2.13thespaceslp（r）
2.14lebesgueintegrablefunctionsonrn
2.15convolution
2.16exercises

chapter3hilbertspacesandorthonormalsystems
3.1introduction
3.2innerproductspaces
3.3hilbertspaces
3.4orthogonalandorthonormalsystems
3.5trigonometricfourierseries
3.6orthogonalcomplementsandprojections
3.7linearfunctionalsandtherieszrepresentationtheorem
3.8exercises

chapter4linearoperatorsonhilbertspaces
4.1introduction
4.2examplesofoperators
4.3bilinearfunctionalsandquadraticforms
4.4adjointandseif-adjointoperators
4.5invertible,normal,isometric,andunitaryoperators
4.6positiveoperators
4.7projectionoperators
4.8compactoperators
4.9eigenvaluesandeigenvectors
4.10spectraldecomposition
4.11unboundedoperators
4.12exercises

chapter5applicationstointegralanddifferentialequations
5.1introduction
5.2basicexistencetheorems
5.3fredholmintegralequations
5.4methodofsuccessiveapproximations
5.5volterraintegralequations
5.6methodofsolutionforaseparablekernel
5.7volterraintegralequationsofthefirstkindandabel'sintegralequation
5.8ordinarydifferentialequationsanddifferentialoperators
5.9sturm-liouvillesystems
5.10inversedifferentialoperatorsandgreen'sfunctions
5.11thefouriertransform
5.12applicationsofthefouriertransformtoordinarydifferentialequationsandintegralequations
6.13exercises

chapter6generalizedfunctionsandpartialdifferentialequations
6.1introduction
6.2distributions
6.3*sobolevspaces
6.4fundamentalsolutionsandgreen'sfunctionsforpartialdifferentialequations
6.5weaksolutionsofellipticboundaryvalueproblems
6.6examplesofapplicationsofthefouriertransformtopartialdifferentialequations
6.7exercises

chapter7mathematicalfoundationsof@uantummechanics
7.1introduction
7.2basicconceptsandequationsofclassicalmechanicspoisson'sbracketsinmechanics
7.3basicconceptsandpostulatesofquantummechanics
7.4theheisenberguncertaintyprinciple
7.5theschrodingerequationofmotion
7.6theschrodingerpicture
7.7theheisenbergpictureandtheheisenbergequationofmotion
7.8theinteractionpicture
7.9thelinearharmonicoscillator
7.10angularmomentumoperators
7.11thediracrelativisticwaveequation
7.12exercises

chapter8waveletsandwavelettransforms
8.1briefhistoricalremarks
8.2continuouswavelettransforms
8.3thediscretewavelettransform
8.4multirosolutionanalysisandorthonormalbasesofwavelets
8.5examplesoforthonormalwavelets
8.6exercises

chapter9optimizationproblemsandothermiscellaneousapplications
9.1introduction
9.2thegateauxandfrechetdifferentials
9.3optimizationproblemsandtheeuler-lagrangeequations
9.4minimizationofquadraticfunctionalss0s
9.5variationalinequalitiess07
9.6optimalcontrolproblemsfordynamicalsystems
9.7approximationtheory
9.8theshannonsamplingtheorem
9.9linearandnonlinearstability
9.10bifurcationtheory
9.11exercises
hintsandanswerstoselectedexercises
bibliography
index