半經典分析 (英文) 瑪西耶.茲沃斯基 9787040612592 【台灣高等教育出版社】
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物品所在地：中國大陸
原出版社：高等教育
物品所在地：中國大陸
原出版社：高等教育
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| *完成訂單後正常情形下約兩周可抵台。 *本賣場提供之資訊僅供參考，以到貨標的為正確資訊。 印行年月：202402*若逾兩年請先於私訊洽詢存貨情況，謝謝。 台灣(台北市)在地出版社，每筆交易均開具統一發票，祝您中獎最高1000萬元。 書名：半經典分析 (英文) ISBN：9787040612592 出版社：高等教育 著編譯者：瑪西耶.茲沃斯基 頁數：431 所在地：中國大陸 *此為代購商品 書號：1625187 可大量預訂，請先連絡。 內容簡介 半經典分析提供了基於經典量子（粒子波）對應關係的偏微分方程技術。這些技術包括幾何光學和Wentzel-Kramers-Brillouin近似等著名工具。本書研究的問題包括高能特徵值漸近性和演化方程解的有效動力學。從數學的角度看，半經典分析是微局部分析的一個分支，廣義上講，是將調和分析和辛幾何應用於線性和非線性偏微分方程的研究。本書旨在作為研究生級別的教材，向讀者介紹偏微分方程中的半經典和微局部方法。它在後面的章節中增加了許多專門的高級主題，這些主題提供了與當前研究文獻的聯繫。目錄 PrefaceChapter 1 Introduction §1 1 Basic themes §1 2 Classical and quantum mechanics §1 3 Overview §1 4 Notes Part 1 BASIC THEORY Chapter 2 Symplectic geometry and analysis §2 1 Flows §2 2 Symplectic structure on R2n §2 3 Symplectic mappings §2 4 Hamiltonian vector fields §2 5 Lagrangian submanifolds §2 6 Notes Chapter 3 Fourier transform， stationary phase §3 1 Fourier transform on l §3 2 Fourier transform on l1 §3 3 Semiclassical Fourier transform §3 4 Stationary phase in one dimension §3 5 Stationary phase in higher dimensions §3 6 Oscillatory integrals §3 7 Notes Chapter 4 Semiclassical quantization §4 1 Definitions §4 2 Quantization formulas §4 3 Composition， asymptotic expansions §4 4 Symbol classes §4 5 Operators on L2 §4 6 Compactness §4 7 Inverses， G~rding inequalities §4 8 Notes Part 2 APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS Chapter 5 Semiclassical defect measures §5 1 Construction， examples §5 2 Defect measures and PDE §5 3 Damped wave equation §5 4 Notes Chapter 6 Eigenvalues and eigenfunctions §6 1 The harmonic oscillator §6 2 Symbols and eigenfunctions §6 3 Spectrum and resolvents §6 4 Weyl's Law §6 5 Notes Chapter 7 Estimates for solutions of PDE §7 1 Classically forbidden regions §7 2 Tunneling §7 3 Order of vanishing §7 4 L estimates for quasimodes §7 5 Schauder estimates §7 6 Notes 3 ADVANCED THEORY AND APPLICATIONS Chapter 8 More on the symbol calculus §8 1 Beals's Theorem §8 2 Real exponentiation of operators §8 3 Generalized Sobolev spaces §8 4 Wavefront sets， essential support， and microlocality §8 5 Notes Chapter 9 Changing variables §9 1 Invariance， half-densities §9 2 Changing symbols §9 3 Invariant symbol classes §9 4 Notes Chapter 10 Fourier integral operators §10 1 Operator dynamics §10 2 An integral representation formula §10 3 Strichartz estimates §10 4 Lp estimates for quasimodes §10 5 Notes Chapter 11 Quantum and classical dynamics §11 1 Egorov's Theorem §11 2 Quantizing syniplectic mappings §11 3 Quantizing linear symplectic mappings §11 4 Egorov's Theorem for longer times §11 5 Notes Chapter 12 Normal forms §12 1 Overview §12 2 Normal forms: real symbols §12 3 Propagation of singularities §12 4 Normal forms: complex symbols §12 5 Quasimodes， pseudospectra §12 6 Notes Chapter 13 The FBI transform §13 1 Motivation §13 2 Complex analysis §13 3 FBI transforms and Bergman kernels §13 4 Quantization and Toeplitz operators §13 5 Applications §13 6 Notes Part 4 SEMICLASSICAL ANALYSIS ON MANIFOLDS Chapter 14 Manifolds §14 1 Definitions， examples §14 2 Pseudodifferential operators on manifolds §14 3 SchrSdinger operators on manifolds §14 4 Notes Chapter 15 Quantum ergodicity §15 1 Classical ergodicity §15 2 A weak Egorov Theorem §15 3 Weyl's Law generalized §15 4 Quantum ergodic theorems §15 5 Notes Part 5 APPENDICES Appendix A Notation §A 1 Basic notation §A 2 Functions， differentiation §A 3 Operators §A 4 Estimates §A 5 Symbol classes Appendix B Differential forms §B 1 Definitions §B 2 Push-forwards and pull-backs §B 3 Poincare's Lemma §B 4 Differential forms on manifolds Appendix C Functional analysis §C 1 Operator theory §C 2 Spectral theory §C 3 Trace class operators Appendix D Fredholm theory §D 1 Grushin problems §D 2 Fredholm operators §D 3 Meromorphic continuation Bibliography Index 詳細資料或其他書籍請至台灣高等教育出版社查詢，查後請於PChome商店街私訊告知ISBN或書號，我們即儘速上架。 |
