相空间中的调和分析
相空间中的调和分析封面图

相空间中的调和分析

(美) 福兰地, 著

出版社:世界图书出版公司北京公司

年代:2009

定价:35.0

书籍简介:

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。

书籍目录:

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

内容摘要:

  Thephrase"harmonicanalysisinphasespace"isaconciseifsomewhatinadequatenamefortheareaofanalysisonRnthatinvolvestheHeisenberggroup,quantization,theWeyloperationalcalculus,themetaplecticrepresentation,wavepackets,andrelatedconcepts:itismeanttosuggestanalysisontheconfigurationspaceRndonebyworkinginthephasespaceRn×Rn.Theideasthatfallunderthisrubrichaveoriginatedinseveraldifferentfields--Fourieranalysis,partialdifferentialequations,mathematicalphysics,representationtheory,andnumbertheory,amongothers.Asaresult,althoughtheseideasareindividuallywellknowntoworkersinsuchfields,theirclosekinshipandthecross-fertilizationtheycanprovidehaveoftenbeeninsufficientlyappreciated.Oneoftheprincipalobjectivesofthismonographistogiveacoherentaccountofthismaterial,comprisingnotjustanefficienttourofthemajoravenuesbutalsoanexplorationofsomepicturesquebyways.

书籍规格:

书籍详细信息
书名相空间中的调和分析站内查询相似图书
9787510005428
如需购买下载《相空间中的调和分析》pdf扫描版电子书或查询更多相关信息,请直接复制isbn,搜索即可全网搜索该ISBN
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

书籍信息归属:

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。