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Field name	Details
Dewey Class	515.2433 (DDC 23)
Title	Fourier Integral Operators ([Ebook]) / by J.J. Duistermaat.
Author	Duistermaat, Johannes Jisse , 1942-
Other name(s)	SpringerLink (Online service)
Publication	Boston : Birkhäuser , 2011.
Physical Details	XI, 142 pages : online resource.
Series	Modern Birkhäuser classics
ISBN	9780817681081
Summary Note	This volume is a useful introduction to the subject of Fourier integral operators and is based on the author's classic set of notes. Covering a range of topics from HÃ¶rmander's exposition of the theory, Duistermaat approaches the subject from symplectic geometry and includes applications to hyperbolic equations (= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is suitable for mathematicians and (theoretical) physicists with an interest in (linear) partial differential equations, especially in wave propagation, resp. WKB-methods. Familiarity with analysis (distributions and Fourier transformation) and differential geometry is useful. Additionally, this book is designed for a one-semester introductory course on Fourier integral operators aimed at a broad audience. This book remains a superb introduction to the theory of Fourier integral operators. While there are further advances discussed in other sources, this book can still be recommended as perhaps the very best place to start in the study of this subject. âSIAM Review This book is still interesting, giving a quick and elegant introduction to the field, more adapted to nonspecialists. âZentralblatt MATH The book is completed with applications to the Cauchy problem for strictly hyperbolic equations and caustics in oscillatory integrals. The reader should have some background knowledge in analysis (distributions and Fourier transformations) and differential geometry. Acta Sci. Math.:
Contents note	Preface -- 0. Introduction -- 1. Preliminaries -- 1.1 Distribution densities on manifolds -- 1.2 The method of stationary phase -- 1.3 The wave front set of a distribution -- 2. Local Theory of Fourier Integrals -- 2.1 Symbols -- 2.2 Distributions defined by oscillatory integrals -- 2.3 Oscillatory integrals with nondegenerate phase functions -- 2.4 Fourier integral operators (local theory) -- 2.5 Pseudodifferential operators in Rn -- 3. Symplectic Differential Geometry -- 3.1 Vector fields -- 3.2 Differential forms -- 3.3 The canonical 1- and 2-form T* (X) -- 3.4 Symplectic vector spaces -- 3.5 Symplectic differential geometry -- 3.6 Lagrangian manifolds -- 3.7 Conic Lagrangian manifolds -- 3.8 Classical mechanics and variational calculus -- 4. Global Theory of Fourier Integral Operators -- 4.1 Invariant definition of the principal symbol -- 4.2 Global theory of Fourier integral operators -- 4.3 Products with vanishing principal symbol -- 4.4 L2-continuity -- 5. Applications -- 5.1 The Cauchy problem for strictly hyperbolic differential operators with C-infinity coefficients -- 5.2 Oscillatory asymptotic solutions. Caustics -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-8176-8108-1
Links to Related Works	Subject References: Differential equations, Partial . Fourier Analysis . Integral Equations . Operator Theory . Partial differential equations . Authors: Duistermaat, Johannes Jisse 1942- . Corporate Authors: SpringerLink (Online service) . Series: Modern Birkhäuser classics . Classification: 515.2433 (DDC 23) .

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Fourier Integral Operators

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