XViii TABLE OF CONTENTS CHAPTER VI. GEOMETRIC ASPECTS OF DISTRIBUTIONS 305 §1. Elementary functorial properties of distributions 305 §2. Traces and characters 316 §3. The wave front set 324 §4. Lagrangian distributions 342 §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 SEMI-SIMPLE LIE GROUPS 388 CHAPTER VII. COMPOUND ASYMPTOTICS 399 §0. Introduction 399 §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 Bernstein's theorem 425 Appendix to Section 5 of Chapter VII 429 §6. Behavior near caustics 434 §7. Iterated St and S20 singularities, computations 447 §8. Proofs of the normal forms 456 §9. Behavior near caustics (continued) 462 APPENDIX II. VARIOUS FUNCTORIAL CONSTRUCTIONS 469 §1. The category of smooth vector bundles 469 §2. The fiber product 4 7 2 INDEX 477
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