## Geometric AsymptoticsSymplectic geometry and the theory of Fourier integral operators are modern manifestations of themes that have occupied a central position in mathematical thought for the past three hundred years - the relations between the wave and the corpuscular theories of light. The purpose of this book is to develop these themes, and present some of the recent advances, using the language of differential geometry as a unifying influence. |

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### Contents

MORSES LEMMA AND SOME GENERALIZATIONS | 16 |

GEOMETRICAL OPTICS | 71 |

SYMPLECTIC GEOMETRY | 109 |

GEOMETRIC QUANTIZATION | 213 |

GEOMETRIC ASPECTS OF DISTRIBUTIONS | 305 |

2 Traces and characters | 316 |

3 The wave front set | 324 |

4 Lagrangian distributions | 342 |

1 The asymptotic Fourier transform | 400 |

2 The frequency set | 404 |

3 Functorial properties of compound asymptotics | 409 |

4 The symbol calculus | 414 |

5 Pointwise behavior of compound asymptotics and Bernsteins theorem | 425 |

Appendix to Section 5 of Chapter VII | 429 |

6 Behavior near caustics | 434 |

7 Iterated S1 and S2o singilarities computations | 447 |

5 The symbol calculus | 354 |

Appendix to Section 5 | 363 |

6 Fourier intergral operators | 364 |

7 The transport equation | 373 |

8 Some applications to spectral theory | 379 |

APPENDIX TO CHAPTER VI THE PLANCHEREL FORMULA FOR THE COMPLEX SEMISIMPLE LIE GROUPS | 388 |

COMPOUND ASYMPTOTICS | 399 |

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