An introduction to semiclassical and microlocal analysis / André Martinez.
Series UniversitextEditor: New York : Springer, c2002Descripción: viii, 190 p. ; 25 cmISBN: 0387953442 (alk. paper)Tema(s): Microlocal analysis | Quantum theoryOtra clasificación: 35A27 (35-01 35Q40 35S05 47G30 58J15 58J40) Recursos en línea: Publisher descriptionPreface v 1 Introduction [1] 1.1 A Short Review of Classical Mechanics [1] 1.2 Basic Notions of Quantum Mechanics [3] 1.3 Semiclassical Analysis [7] 1.4 About History [8] 2 Semiclassical Pseudodifferential Calculus [9] 2.1 Motivation and Notation [9] 2.2 Spaces of Symbols [10] 2.3 Semiclassical Expansions of Symbols [13] 2.4 Oscillatory Integrals [17] 2.5 Pseudodifferential Operators [22] 2.6 Composition [27] 2.7 Change of Quantization - Symbolic Calculus [36] 2.8 L2-Continuity [43] 2.9 A First Application: The Frequency Set [51] 2.10 Exercises and Problems [55] 3 Microlocalization [69] 3.1 The Global FBI Transform [69] 3.2 Microsupport [73] 3.3 Action of the FBI Transform on ψ DOs [77] 3.4 Action of the FBI Transform on FIOs [79] 3.5 Microlocal Exponential Estimates [87] 3.6 Exercises and Problems [96] 4 Applications to the Solutions of Analytic Linear PDEs [105] 4.1 Projection of the Microsupport [105] 4.2 Characteristic Set and Microsupport [105] 4.3 Propagation of the Microsupport [114] 4.4 Microhyperbolicity [125] 4.5 Boundary Value Problems [130] 4.6 Exercises and Problems [132] 5 Complements: Symplectic Aspects [141] 5.1 The Canonical Symplectic Form on R2n [141] 5.2 Symplectic Transformations [142] 5.3 Hamilton Field [144] 5.4 Lagrangian Submanifolds [146] 5.5 Applications to the Study of PDEs [147] 5.6 Exercises and Problems [161] 6 Appendix: List of Formulae [169] 6.1 Change of Quantization [169] 6.1.1 Semiclassical Calculus [169] 6.1.2 Nonsemiclassical Calculus [170] 6.2 Composition Formulae [170] 6.2.1 Semiclassical Calculus [170] 6.2.2 Nonsemiclassical Calculus [170] 6.3 Symbol of the Adjoint and Transpose Operator [171] 6.3.1 Semiclassical Calculus [171] 6.3.2 Nonsemiclassical Calculus [172] 6.4 Symbol of a Commutator [172] 6.5 Functional Calculus [172] 6.6 Fourier-Bros-Iagolnitzer Transform [172] 6.7 Microlocal Exponential Estimates [173] 6.8 Agmon Estimates [173] Bibliography [175] Index [183] List of Notation [189]
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 35 M385 (Browse shelf) | Available | A-9280 |
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Incluye referencias bibliográficas (p. 175-181) e índice.
Preface v --
1 Introduction [1] --
1.1 A Short Review of Classical Mechanics [1] --
1.2 Basic Notions of Quantum Mechanics [3] --
1.3 Semiclassical Analysis [7] --
1.4 About History [8] --
2 Semiclassical Pseudodifferential Calculus [9] --
2.1 Motivation and Notation [9] --
2.2 Spaces of Symbols [10] --
2.3 Semiclassical Expansions of Symbols [13] --
2.4 Oscillatory Integrals [17] --
2.5 Pseudodifferential Operators [22] --
2.6 Composition [27] --
2.7 Change of Quantization - Symbolic Calculus [36] --
2.8 L2-Continuity [43] --
2.9 A First Application: The Frequency Set [51] --
2.10 Exercises and Problems [55] --
3 Microlocalization [69] --
3.1 The Global FBI Transform [69] --
3.2 Microsupport [73] --
3.3 Action of the FBI Transform on ψ DOs [77] --
3.4 Action of the FBI Transform on FIOs [79] --
3.5 Microlocal Exponential Estimates [87] --
3.6 Exercises and Problems [96] --
4 Applications to the Solutions of Analytic Linear PDEs [105] --
4.1 Projection of the Microsupport [105] --
4.2 Characteristic Set and Microsupport [105] --
4.3 Propagation of the Microsupport [114] --
4.4 Microhyperbolicity [125] --
4.5 Boundary Value Problems [130] --
4.6 Exercises and Problems [132] --
5 Complements: Symplectic Aspects [141] --
5.1 The Canonical Symplectic Form on R2n [141] --
5.2 Symplectic Transformations [142] --
5.3 Hamilton Field [144] --
5.4 Lagrangian Submanifolds [146] --
5.5 Applications to the Study of PDEs [147] --
5.6 Exercises and Problems [161] --
6 Appendix: List of Formulae [169] --
6.1 Change of Quantization [169] --
6.1.1 Semiclassical Calculus [169] --
6.1.2 Nonsemiclassical Calculus [170] --
6.2 Composition Formulae [170] --
6.2.1 Semiclassical Calculus [170] --
6.2.2 Nonsemiclassical Calculus [170] --
6.3 Symbol of the Adjoint and Transpose Operator [171] --
6.3.1 Semiclassical Calculus [171] --
6.3.2 Nonsemiclassical Calculus [172] --
6.4 Symbol of a Commutator [172] --
6.5 Functional Calculus [172] --
6.6 Fourier-Bros-Iagolnitzer Transform [172] --
6.7 Microlocal Exponential Estimates [173] --
6.8 Agmon Estimates [173] --
Bibliography [175] --
Index [183] --
List of Notation [189] --
MR, MR1872698
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