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Geometric asymptotics / Victor Guillemin, Shlomo Sternberg

Auteur principal : Guillemin, Victor, 1937-, AuteurCo-auteur : Sternberg, Shlomo, 1936-, AuteurType de document : MonographieCollection : Mathematical surveys, 14Langue : anglais.Pays : Etats Unis.Éditeur : Providence : American Mathematical Society, 1977Description : 1 vol. (XVIII-474 p.) : ill. ; 26 cmISBN : 0821815148.ISSN : 0076-5376.Bibliographie : Notes bibliogr. Index.Sujet MSC : 53C15, Global differential geometry, General geometric structures on manifolds
53-02, Research exposition (monographs, survey articles) pertaining to differential geometry
58Jxx, Global analysis, analysis on manifolds - Partial differential equations on manifolds; differential operators
35B40, Qualitative properties of solutions to partial differential equations, Asymptotic behavior of solutions to PDEs
44-00, General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral transforms
En-ligne : MathSciNet | AMS
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Notes bibliogr. Index

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. (source : AMS)

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