相空间中的调和分析

图书标准信息

• 作者 [美]福兰地 著
• 出版社 世界图书出版公司
• 出版时间 2009-08
• 版次 1
• ISBN 9787510005428
• 定价 35.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 277页
• 正文语种 英语
• 原版书名 Harmonic Analysis in Phase Space

【内容简介】

Thephrase"harmonicanalysisinphasespace"isaconciseifsomewhatinadequatenamefortheareaofanalysisonRnthatinvolvestheHeisenberggroup，quantization，theWeyloperationalcalculus，themetaplecticrepresenta-tion，wavepackets，andrelatedconcepts：itismeanttosuggestanalysisontheconfigurationspaceRndonebyworkinginthephasespaceRnxRn.Theideasthatfallunderthisrubrichaveoriginatedinseveraldifferentfidds——Fourieranalysis，partialdifferentialequations，mathematicalphysics，representationtheory，andnumbertheory，amongothers.

【目录】

Preface
Prologue.SomeMattersofNotation
CHAPTER1.
THEHEISENBERGGROUPANDITSREPRESENTATIONS
1.Backgroundfromphysics
Hamiltonianmechanics，10.Quantummechanics，12.Quantization，15.
2.TheHeisenberggroup
TheautomorphismsoftheHeisenberggroup，19.
3.TheSchrSdingerrepresentation
Theintegratedrepresentation，23.Twistedconvolution，25.
Theuncertaintyprinciple，27.
4.TheFourier-Wignertransform
Radarambiguityfunctions，33.
5.TheStone-vonNeumanntheorem
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.TheCalderSn-Vaillancourttheorems
6.ThesharpGardinginequality
7.TheWickandanti-Wickcorrespondences

CHAPTER3.
WAVEPACKETSANDWAVEFRONTS
1.Wavepacketexpansions
2.Acharacterizationofwavefrontsets
3.AnalyticityandtheFBItransform
4.Gaborexpansions

CHAPPTER4.
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.TheSchrSdingermodel
Theextendedoscillatorsemigroup，234.
2.TheHermitesemigroup
3.NormalizationandtheCayleytransform
4.TheFockmodel
AppendixA.GaussianIntegralsandaLemmaonDeterminants
AppendixB.SomeHilbertSpaceResults
Bibliography
Index