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  • surv14-frnt.pdf

    • Frontmatter

      • Title

      • Copyright page

      • Dedication

      • Preface

      • Notation

      • Contents

    • Chapter I. Introduction. The method of stationary phase

    • Appendix I. Morse's lemma and some generalizations

    • Chapter II. Differential operators and asymptotic solutions

    • Chapter III. Geometrical options

    • Chapter IV. Symplectic geometry

    • Chapter V. Geometric quantization

    • Chapter VI. Geometric aspects of distributions

    • Appendix to Chapter VI. The Plancherel formula for the complex semi-simple Lie groups

    • Chapter VII. Compound asymptotics

    • Appendix II. Various functorial constructions

    • Endmatter

  • surv14-chI.pdf

    • Frontmatter

    • Chapter I. Introduction. The method of stationary phase

    • Appendix I. Morse's lemma and some generalizations

    • Chapter II. Differential operators and asymptotic solutions

    • Chapter III. Geometrical options

    • Chapter IV. Symplectic geometry

    • Chapter V. Geometric quantization

    • Chapter VI. Geometric aspects of distributions

    • Appendix to Chapter VI. The Plancherel formula for the complex semi-simple Lie groups

    • Chapter VII. Compound asymptotics

    • Appendix II. Various functorial constructions

    • Endmatter

  • surv14-appI.pdf

    • Frontmatter

    • Chapter I. Introduction. The method of stationary phase

    • Appendix I. Morse's lemma and some generalizations

    • Chapter II. Differential operators and asymptotic solutions

    • Chapter III. Geometrical options

    • Chapter IV. Symplectic geometry

    • Chapter V. Geometric quantization

    • Chapter VI. Geometric aspects of distributions

    • Appendix to Chapter VI. The Plancherel formula for the complex semi-simple Lie groups

    • Chapter VII. Compound asymptotics

    • Appendix II. Various functorial constructions

    • Endmatter

  • surv14-chII.pdf

    • Frontmatter

    • Chapter I. Introduction. The method of stationary phase

    • Appendix I. Morse's lemma and some generalizations

    • Chapter II. Differential operators and asymptotic solutions

      • 1. Differential operators

      • 2. Asymptotic sections

      • 3. The Luneburg-Lax-Ludwig technique

      • 4. The methods of characteristics

      • 5. Bicharacteristics

      • 6. The transport equation

      • 7. The Maslov cycle and the Bohr-Sommerfeld quantization conditions

    • Chapter III. Geometrical options

    • Chapter IV. Symplectic geometry

    • Chapter V. Geometric quantization

    • Chapter VI. Geometric aspects of distributions

    • Appendix to Chapter VI. The Plancherel formula for the complex semi-simple Lie groups

    • Chapter VII. Compound asymptotics

    • Appendix II. Various functorial constructions

    • Endmatter

  • surv14-chIII.pdf

    • Frontmatter

    • Chapter I. Introduction. The method of stationary phase

    • Appendix I. Morse's lemma and some generalizations

    • Chapter II. Differential operators and asymptotic solutions

    • Chapter III. Geometrical optics

      • 1. The laws of refraction and reflection

      • 2. Focusing and Magnification

      • 3. Hamilton's method

      • 4. First order optics

      • 5. The Seidel aberrations

      • 6. The asymptotic solution of Maxwell's equations

    • Chapter IV. Symplectic geometry

    • Chapter V. Geometric quantization

    • Chapter VI. Geometric aspects of distributions

    • Appendix to Chapter VI. The Plancherel formula for the complex semi-simple Lie groups

    • Chapter VII. Compound asymptotics

    • Appendix II. Various functorial constructions

    • Endmatter

  • surv14-chIV.pdf

    • Frontmatter

    • Chapter I. Introduction. The method of stationary phase

    • Appendix I. Morse's lemma and some generalizations

    • Chapter II. Differential operators and asymptotic solutions

    • Chapter III. Geometrical options

    • Chapter IV. Symplectic geometry

      • 1. The Darboux-Weinstein theorem

      • 2. Symplectic vector spaces

      • 3. The cross index and the Maslov class

      • 4. Functorial properties of Lagrangian submanifolds

      • 5. Local parametrizations of Lagrangian submanifolds

      • 6. Periodic Hamiltonian systems

      • 7. Homogeneous symplectic spaces

      • 8. Multisymplectic structures and the calculus of variations

    • Chapter V. Geometric quantization

    • Chapter VI. Geometric aspects of distributions

    • Appendix to Chapter VI. The Plancherel formula for the complex semi-simple Lie groups

    • Chapter VII. Compound asymptotics

    • Appendix II. Various functorial constructions

    • Endmatter

  • surv14-chV.pdf

    • Frontmatter

    • Chapter I. Introduction. The method of stationary phase

    • Appendix I. Morse's lemma and some generalizations

    • Chapter II. Differential operators and asymptotic solutions

    • Chapter III. Geometrical options

    • Chapter IV. Symplectic geometry

    • Chapter V. Geometric quantization

      • 1. Curvature forms and vector bundles

      • 2. The group of automorphisms of an Hermitian line bundle

      • 3. Polarizations

      • 4. Metalinear manifolds and half forms

      • 5. Metaplectic manifolds

      • 6. The pairing of half form sections

      • 7. The metaplectic representation

      • 8. Some examples

    • Chapter VI. Geometric aspects of distributions

    • Appendix to Chapter VI. The Plancherel formula for the complex semi-simple Lie groups

    • Chapter VII. Compound asymptotics

    • Appendix II. Various functorial constructions

    • Endmatter

  • surv14-chVI.pdf

    • Frontmatter

    • Chapter I. Introduction. The method of stationary phase

    • Appendix I. Morse's lemma and some generalizations

    • Chapter II. Differential operators and asymptotic solutions

    • Chapter III. Geometrical options

    • Chapter IV. Symplectic geometry

    • Chapter V. Geometric quantization

    • Chapter VI. Geometric aspects of distributions

      • 1. Elementary functorial properties of distributions

      • 2. Traces and characters

      • 3. The wave front set

      • 4. Lagrangian distributions

      • 5. The symbol calculus

      • Appendix to Section 5

      • 6. Fourier integral operators

      • 7. The transport equation

      • 8. Some applications to spectral theory

    • Appendix to Chapter VI. The Plancherel formula for the complex semi-simple Lie groups

    • Chapter VII. Compound asymptotics

    • Appendix II. Various functorial constructions

    • Endmatter

  • surv14-app-to-VI.pdf

    • Frontmatter

    • Chapter I. Introduction. The method of stationary phase

    • Appendix I. Morse's lemma and some generalizations

    • Chapter II. Differential operators and asymptotic solutions

    • Chapter III. Geometrical options

    • Chapter IV. Symplectic geometry

    • Chapter V. Geometric quantization

    • Chapter VI. Geometric aspects of distributions

    • Appendix to Chapter VI. The Plancherel formula for the complex semi-simple Lie groups

    • Chapter VII. Compound asymptotics

    • Appendix II. Various functorial constructions

    • Endmatter

  • surv14-chVII.pdf

    • Frontmatter

    • Chapter I. Introduction. The method of stationary phase

    • Appendix I. Morse's lemma and some generalizations

    • Chapter II. Differential operators and asymptotic solutions

    • Chapter III. Geometrical options

    • Chapter IV. Symplectic geometry

    • Chapter V. Geometric quantization

    • Chapter VI. Geometric aspects of distributions

    • Appendix to Chapter VI. The Plancherel formula for the complex semi-simple Lie groups

    • Chapter VII. Compound asymptotics

      • 0. Introduction

      • 1. The asymptotic Fourier transform

      • 2. The frequency set

      • 3. Functorial properties of compound asymptotics

      • 4. The symbol calculus

      • 5. Pointwise behavior of compound asymptotics and Bernstein's theorem

      • Appendix to Section 5 of Chapter VII

      • 6. Behavior near caustics

      • 7. Iterated S_1 and S{_2,0} singularities, computations

      • 8. Proofs of the normal forms

      • 9. Behavior near caustics (continued)

    • Appendix II. Various functorial constructions

    • Endmatter

  • surv14-appII.pdf

    • Frontmatter

    • Chapter I. Introduction. The method of stationary phase

    • Appendix I. Morse's lemma and some generalizations

    • Chapter II. Differential operators and asymptotic solutions

    • Chapter III. Geometrical options

    • Chapter IV. Symplectic geometry

    • Chapter V. Geometric quantization

    • Chapter VI. Geometric aspects of distributions

    • Appendix to Chapter VI. The Plancherel formula for the complex semi-simple Lie groups

    • Chapter VII. Compound asymptotics

    • Appendix II. Various functorial constructions

      • 1. The category of smooth vector bundles

      • 2. The fiber product

    • Endmatter

  • surv14-bck.pdf

    • Frontmatter

    • Chapter I. Introduction. The method of stationary phase

    • Appendix I. Morse's lemma and some generalizations

    • Chapter II. Differential operators and asymptotic solutions

    • Chapter III. Geometrical options

    • Chapter IV. Symplectic geometry

    • Chapter V. Geometric quantization

    • Chapter VI. Geometric aspects of distributions

    • Appendix to Chapter VI. The Plancherel formula for the complex semi-simple Lie groups

    • Chapter VII. Compound asymptotics

    • Appendix II. Various functorial constructions

    • Endmatter

      • Index

Nội dung

Geometric Asymptotics Revised Edition Victor Guillemin Shlomo Sternberg Mathematical Surveys and Monographs Volume 14 American Mathematical Society

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