出版社：世界图书出版公司北京公司
年代：2009
定价：35.0
本书是相空间中调和分析方面的一本专著。主要介绍了Heisenberg群表示定理，拟微分算子的Weyl运算，Weyl运算框架下的波包变换，及Metaplectic表示，并收录了该领域近年来的一些研究成果。本书内容丰富，行文流畅，相信此书的出版将会给致力于此专业的学者提供极大帮助。本书读者对象为数学专业的研究生和教学工作者。
Preface
Prologue.SomeMattersofNotation
CHAPTER1.THEHEISENBERGGROUPANDITSREPRESENTATIONS
1.Backgroundfromphysics
Hamiltonianmechanics,10.Quantummechanics,12.Quantization,15.
2.TheHeisenberggroup
TheautomorphismsoftheHeisenberggroup,19.
3.TheSchr~Sdingerrepresentation
Theintegratedrepresentation,23.Twistedconvolution,25.
Theuncertaintyprinciple,27.
4.TheFourier-Wignertransform
Radarambiguityfunctions,33.
5.TheStone-yonNeumanntheorem
ThegroupFouriertransform,37.
6.TheFock-Bargmannrepresentation
Somemotivationandhistory,47.
7.Hermitefunctions
8.TheWignertransform
9.TheLaguerreconnection
10.Thenilmanifoldrepresentation
11.Postscripts
CHAPTER2.QUANTIZATIONANDPSEUDODIFFERENTIALOPERATORS
1.TheWeylcorrespondence
Covarianceproperties,83.Symbolclasses,86.Miscellaneousremarks
andexamples,90.
2.TheKohn-Nirenbergcorrespondence
3.Theproductformula
4.Basicpseudodifferentialtheory
Wavefrontsets,118.
5.TheCalder6n-VaiUancourttheorems
6.ThesharpG~rdinginequality
7.TheWickandanti-Wickcorrespondences
CHAPTER3.WAVEPACKETSANDWAVEFRONTS
1.Wavepacketexpansions
2.Acharacterizationofwavefrontsets
3.AnalyticityandtheFBItransform
4.Gaborexpansions
CHAPTER4.THEMETAPLECTICREPRESENTATION
1.Symplecticlinearalgebra
2.Constructionofthemetaplecticrepresentation
TheFockmodel,180.
3.Theinfinitesimalrepresentation
4.Otheraspectsofthemetaplecticrepresentation
Integralformulas,191.Irreduciblesubspaces,194.Dependenceon
Plancksconstant,195.Theextendedmetaplecticrepresentation,196.
TheGroenewold-vanHovetheorems,197.Someapplications,199.
5.Gaussiansandthesymmetricspace
CharacterizationsofGaussians,206.
6.Thediscmodel
7.Variantsandanalogues
Restrictionsofthemetaplecticrepresentation,216.U(n,n)asacomplex
symplecticgroup,217.Thespinrepresentation,220.
CHAPTER5.THEOSCILLATORSEMIGROUP
1.TheSchrodingermodel
Theextendedoscillatorsemigroup,234.
2.TheHermitesemigroup
3.NormalizationandtheCayleytransform
4.TheFockmodel
AppendixA.GaussianIntegralsandaLemmaonDeterminants
AppendixB.SomeHilbertSpaceResults
Bibliography
Index
Thephrase"harmonicanalysisinphasespace"isaconciseifsomewhatinadequatenamefortheareaofanalysisonRnthatinvolvestheHeisenberggroup,quantization,theWeyloperationalcalculus,themetaplecticrepresentation,wavepackets,andrelatedconcepts:itismeanttosuggestanalysisontheconfigurationspaceRndonebyworkinginthephasespaceRn×Rn.Theideasthatfallunderthisrubrichaveoriginatedinseveraldifferentfields--Fourieranalysis,partialdifferentialequations,mathematicalphysics,representationtheory,andnumbertheory,amongothers.Asaresult,althoughtheseideasareindividuallywellknowntoworkersinsuchfields,theirclosekinshipandthecross-fertilizationtheycanprovidehaveoftenbeeninsufficientlyappreciated.Oneoftheprincipalobjectivesofthismonographistogiveacoherentaccountofthismaterial,comprisingnotjustanefficienttourofthemajoravenuesbutalsoanexplorationofsomepicturesquebyways.
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| 书名 | 相空间中的调和分析站内查询相似图书 | ||
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| 出版地 | 北京 | 出版单位 | 世界图书出版公司北京公司 |
| 版次 | 1版 | 印次 | 1 |
| 定价(元) | 35.0 | 语种 | 英文 |
| 尺寸 | 14 | 装帧 | 平装 |
| 页数 | 印数 | 1000 | |
相空间中的调和分析是世界图书出版公司北京公司于2009.08出版的中图分类号为 O186.14 的主题关于 相空间－调和分析－研究生－教材－英文 的书籍。