04241nam a22004935i 4500 978-0-8176-8108-1 DE-He213 20260521092033.0 cr nn 008mamaa 110222s2011 xxu| s |||| 0|eng d 9780817681081 99780817681081 10.1007/978-0-8176-8108-1 doi 515.2433 23 Duistermaat, J.J. author. Fourier Integral Operators [electronic resource] / by J.J. Duistermaat. Boston : Birkhäuser Boston, 2011. XI, 142 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Modern Birkhäuser Classics 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. 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 Hörmander'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. -SIAM Review This book is still interesting, giving a quick and elegant introduction to the field, more adapted to nonspecialists. -Zentralblatt 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. MATHEMATICS. FOURIER ANALYSIS. INTEGRAL EQUATIONS. OPERATOR THEORY. DIFFERENTIAL EQUATIONS, PARTIAL. MATHEMATICS. FOURIER ANALYSIS. INTEGRAL EQUATIONS. OPERATOR THEORY. PARTIAL DIFFERENTIAL EQUATIONS. SpringerLink (Online service) Springer eBooks Printed edition: 9780817681074 Modern Birkhäuser Classics http://dx.doi.org/10.1007/978-0-8176-8108-1 Ver el texto completo en las instalaciones del CICY ZDB-2-SMA ddc ER 35783 35783 0 0 ddc 0 0 LE CICY CICY EL 2025-10-06 0 515.2433 2025-10-06 08:44:40 2025-10-06 ER