Geometric Asymptotics, Revised edition
About this Title
V. Guillemin and S. Sternberg
Publication: Mathematical Surveys and Monographs
Publication Year 1977: Volume 14
ISBNs: 978-0-8218-1633-2 (print); 978-0-8218-3208-0 (online)
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.
Chapters included in this book are: 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; Chapter IV, Symplectic geometry; Chapter V, Geometric quantization; Chapter VI, Geometric aspects of distribution; Appendix to Chapter VI, The Plancherel formula for the complex semisimple Lie groups; Chapter VII, Compound Asymptotics; Appendix II, Various functorial constructions; Index.
Table of Contents
- I. Introduction. The method of stationary phase
- II. Differential operators and asymptotic solutions
- III. Geometrical optics
- IV. Symplectic geometry
- V. Geometric quantization
- VI. Geometric aspects of distributions
- VII. Compound asymptotics