Geometric Asymptotics

Front Cover
American Mathematical Soc., 1990 - Mathematics - 480 pages
Symplectic 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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

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
8 Proofs of the normal forms
456
9 Behavior near caustics continued
462
VARIOUS FUNCTORIAL CONSTRUCTIONS
469
2 The fiber product
472
INDEX
477
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information