000			04241nam a22004935i 4500
001			978-0-8176-8108-1
003			DE-He213
005			20251006084440.0
007			cr nn 008mamaa
008			110222s2011 xxu| s |||| 0|eng d
020			_a9780817681081
020			_a99780817681081
024	7		_a10.1007/978-0-8176-8108-1 _2doi
082	0	4	_a515.2433 _223
100	1		_aDuistermaat, J.J. _eauthor.
245	1	0	_aFourier Integral Operators _h[electronic resource] / _cby J.J. Duistermaat.
264		1	_aBoston : _bBirkhäuser Boston, _c2011.
300			_aXI, 142 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aModern Birkhäuser Classics
505	0		_aPreface -- 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.
520			_aThis 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.
650		0	_aMATHEMATICS.
650		0	_aFOURIER ANALYSIS.
650		0	_aINTEGRAL EQUATIONS.
650		0	_aOPERATOR THEORY.
650		0	_aDIFFERENTIAL EQUATIONS, PARTIAL.
650	1	4	_aMATHEMATICS.
650	2	4	_aFOURIER ANALYSIS.
650	2	4	_aINTEGRAL EQUATIONS.
650	2	4	_aOPERATOR THEORY.
650	2	4	_aPARTIAL DIFFERENTIAL EQUATIONS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817681074
830		0	_aModern Birkhäuser Classics
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-8108-1 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59850 _d59850