**Mathematical Surveys and Monographs** 1977; 480 pp; softcover Volume: 14 Reprint/Revision History: revised edition 1991 ISBN-10: 0-8218-1633-0 ISBN-13: 978-0-8218-1633-2 List Price: US$96 Member Price: US$76.80 Order Code: SURV/14
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| 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. Reviews "The topic of this nice book can be defined as a geometric approach to the investigation of some analytic problems, especially to the study of Fourier integral operators. These operators are now widely used for the analysis of singularities of solutions of linear partial differential equations and for the study of the spectra of the corresponding operators. In general the book is very interesting and useful for specialists both in analysis and in differential geometry." *-- Mathematical Reviews* |