Fourier integral operators
著者
書誌事項
Fourier integral operators
（Modern Birkhäuser classics）
Birkhäuser , Springer, 2011
Reprint of the 1996 ed
- : pbk
大学図書館所蔵 件 / 全8件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references
"Originally published as Volume 130 in the series Progress in Mathematics"
内容説明・目次
内容説明
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 Hoermander's exposition of the theory, Duistermaat approaches the subject from symplectic geometry and includes application 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, rep. WKB-methods.
目次
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.
「Nielsen BookData」 より