Fourier Integral Operators
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Beschreibung
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.
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 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.
Based on author’s original lecture notes Covers a broad range of topics Useful for both practitioners and students Applications put theory in context Includes supplementary material: sn.pub/extras
Autor*in
J.J. Duistermaat
Themen in »Fourier Integral Operators«
Distribution Fourier transform Fourier transformation Lagragian manifolds Operator Transformation calculus geometry global theory hyperbolic equation integral operators mechanics partial differential equation partial differential equations symplectic differential geometry
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From the reviews:
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.
“Duistermaat’s Fourier Integral Operators had its genesis in a course the author taught at Nijmegen in 1970. … For the properly prepared and properly disposed mathematical audience Fourier Integral Operators is a must. … it is a very important book on a subject that is both deep and broad.” (Michael Berg, The Mathematical Association of America, May, 2011)
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