相空间中的调和分析
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作者[美] 福兰地 著
出版社世界图书出版公司
ISBN9787510005428
出版时间2009-08
版次1
装帧平装
开本16开
纸张胶版纸
页数277页
定价35元
上书时间2024-07-31
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基本信息
书名:相空间中的调和分析
定价：35元
作者:[美] 福兰地 著
出版社：世界图书出版公司
出版日期：2009-08-01
ISBN：9787510005428
字数：
页码：277
版次：1
装帧：平装
开本：24开
商品重量：
编辑推荐
The maipoint of Chapter 2 is the development of the Weyl calculusof pseudodifferential operators.
内容提要
The phrase "harmonic analysis iphase space" is a concise if somewhatinadequate name for the area of analysis oRthat involves the Heisenberggroup，quantization，the Weyl operational calculus，the metaplectic representa-tion，wave packets，and related concepts： it is meant to suggest analysis otheconfiguratiospace Rdone by working ithe phase space Rx Rn. The ideasthat fall under this rubric have originated iseveral different fidds——Fourieranalysis，partial differential equations，mathematical physics，representationtheory，and number theory，among others.
目录
PrefacePrologue. Some Matters of NotationCHAPTER 1.THE HEISENBERG GROUP AND ITS REPRESENTATIONS1. Background from physicsHamiltoniamechanics， 10. Quantum mechanics， 12. Quantization， 15.2. The Heisenberg groupThe automorphisms of the Heisenberg group， 19.3. The SchrSdinger representationThe integrated representation， 23. Twisted convolution， 25.The uncertainty principle， 27.4. The Fourier-Wigner transformRadar ambiguity functions， 33.5. The Stone-voNeumantheoremThe group Fourier transform， 37.6. The Fock-BargmanrepresentationSome motivatioand history， 47.7. Hermite functions8. The Wigner transform9. The Laguerre connection10. The nilmanifold representation11. PostscriptsCHAPTER 2.QUANTIZATION AND PSEUDODIFFERENTIAL OPERATORS1. The Weyl correspondenceCovariance properties， 83. Symbol classes， 86. Miscellaneous remarksand examples， 90.2. The Kohn-Nirenberg correspondence3. The product formula4. Basic pseudodifferential theoryWave front sets， 118.5. The CalderSn-Vaillancourt theorems6. The sharp Garding inequality7. The Wick and anti-Wick correspondencesCHAPTER 3.WAVE PACKETS AND WAVE FRONTS1. Wave packet expansions2. A characterizatioof wave front sets3. Analyticity and the FBI transform4. Gabor expansionsCHAPPTER 4.THE METAPLECTIC REPRESENTATION1. Symplectic linear algebra2. Constructioof the metaplectic representationThe Fock model， 180.3. The infinitesimal representation4. Other aspects of the metaplectic representationIntegral formulas， 191. Irreducible subspaces， 194. Dependence onPlancks constant， 195. The extended metaplectic representation， 196.The Groenewold-vaHove theorems， 197. Some applications， 199.5. Gaussians and the symmetric spaceCharacterizations of Gaussians， 206.6. The disc model7. Variants and analoguesRestrictions of the metaplectic representation， 216. U(n，n) as a complexsymplectic group， 217. The spirepresentation， 220.CHAPTER 5.THE OSCILLATOR SEMIGROUP1. The SchrSdinger modelThe extended oscillator semigroup， 234.2. The Hermite semigroup3. Normalizatioand the Cayley transform4. The Fock modelAppendix A. GaussiaIntegrals and a Lemma oDeterminantsAppendix B. Some Hilbert Space ResultsBibliographyIndex
作者介绍
作者：(美国)福兰地
序言
PrefacePrologue. Some Matters of NotationCHAPTER 1.THE HEISENBERG GROUP AND ITS REPRESENTATIONS1. Background from physicsHamiltoniamechanics， 10. Quantum mechanics， 12. Quantization， 15.2. The Heisenberg groupThe automorphisms of the Heisenberg group， 19.3. The SchrSdinger representationThe integrated representation， 23. Twisted convolution， 25.The uncertainty principle， 27.4. The Fourier-Wigner transformRadar ambiguity functions， 33.5. The Stone-voNeumantheoremThe group Fourier transform， 37.6. The Fock-BargmanrepresentationSome motivatioand history， 47.7. Hermite functions8. The Wigner transform9. The Laguerre connection10. The nilmanifold representation11. PostscriptsCHAPTER 2.QUANTIZATION AND PSEUDODIFFERENTIAL OPERATORS1. The Weyl correspondenceCovariance properties， 83. Symbol classes， 86. Miscellaneous remarksand examples， 90.2. The Kohn-Nirenberg correspondence3. The product formula4. Basic pseudodifferential theoryWave front sets， 118.5. The CalderSn-Vaillancourt theorems6. The sharp Garding inequality7. The Wick and anti-Wick correspondencesCHAPTER 3.WAVE PACKETS AND WAVE FRONTS1. Wave packet expansions2. A characterizatioof wave front sets3. Analyticity and the FBI transform4. Gabor expansionsCHAPPTER 4.THE METAPLECTIC REPRESENTATION1. Symplectic linear algebra2. Constructioof the metaplectic representationThe Fock model， 180.3. The infinitesimal representation4. Other aspects of the metaplectic representationIntegral formulas， 191. Irreducible subspaces， 194. Dependence onPlancks constant， 195. The extended metaplectic representation， 196.The Groenewold-vaHove theorems， 197. Some applications， 199.5. Gaussians and the symmetric spaceCharacterizations of Gaussians， 206.6. The disc model7. Variants and analoguesRestrictions of the metaplectic representation， 216. U(n，n) as a complexsymplectic group， 217. The spirepresentation， 220.CHAPTER 5.THE OSCILLATOR SEMIGROUP1. The SchrSdinger modelThe extended oscillator semigroup， 234.2. The Hermite semigroup3. Normalizatioand the Cayley transform4. The Fock modelAppendix A. GaussiaIntegrals and a Lemma oDeterminantsAppendix B. Some Hilbert Space ResultsBibliographyIndex
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