• Mathematics

Fourier Integral Operators


Author: J.J. Duistermaat
Publisher: Springer Science & Business Media
ISBN: 9780817681081
Category: Mathematics
Page: 142
View: 6762
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.

    • Mathematics

Mathematics Past and Present Fourier Integral Operators


Author: J.J. Duistermaat,Victor W Guillemin,Jochen Brüning,L. Hörmander
Publisher: Springer Science & Business Media
ISBN: 9783540567417
Category: Mathematics
Page: 283
View: 3670
The reader will feel the inspiration, freshness and enthusiasm of a new breakthrough in mathematical thought in the 4 seminal papers presented here for the first time ever in one volume. The 4 papers by Duistermaat, Guillemin and Hörmander have been a milestone in the development of this field. The new ideas presented in these papers - in a very lucid and accessible form - became the foundation on which more and more abstract theories were built in the relentless march towards even better and more detailed results. The detailed introductory comments by V. Guillemin are the final touch in a volume that combines the basic motivation and ideas of the early sources with the present state of F.I.O. thus bridging the gap between the past and present.


    • Mathematics

Introduction to Pseudodifferential and Fourier Integral Operators

Pseudodifferential Operators
Author: Jean-François Treves
Publisher: Springer Science & Business Media
ISBN: 1468487809
Category: Mathematics
Page: 299
View: 8237
I have tried in this book to describe those aspects of pseudodifferential and Fourier integral operator theory whose usefulness seems proven and which, from the viewpoint of organization and "presentability," appear to have stabilized. Since, in my opinion, the main justification for studying these operators is pragmatic, much attention has been paid to explaining their handling and to giving examples of their use. Thus the theoretical chapters usually begin with a section in which the construction of special solutions of linear partial differential equations is carried out, constructions from which the subsequent theory has emerged and which continue to motivate it: parametrices of elliptic equations in Chapter I (introducing pseudodifferen tial operators of type 1, 0, which here are called standard), of hypoelliptic equations in Chapter IV (devoted to pseudodifferential operators of type p, 8), fundamental solutions of strongly hyperbolic Cauchy problems in Chap ter VI (which introduces, from a "naive" standpoint, Fourier integral operators), and of certain nonhyperbolic forward Cauchy problems in Chapter X (Fourier integral operators with complex phase). Several chapters-II, III, IX, XI, and XII-are devoted entirely to applications. Chapter II provides all the facts about pseudodifferential operators needed in the proof of the Atiyah-Singer index theorem, then goes on to present part of the results of A. Calderon on uniqueness in the Cauchy problem, and ends with a new proof (due to J. J. Kohn) of the celebrated sum-of-squares theorem of L. Hormander, a proof that beautifully demon strates the advantages of using pseudodifferential operators.

    • Mathematics

Fourier Integrals in Classical Analysis


Author: Christopher D. Sogge
Publisher: Cambridge University Press
ISBN: 9780521434645
Category: Mathematics
Page: 236
View: 3803
An advanced monograph concerned with modern treatments of central problems in harmonic analysis.




    • Mathematics

Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces


Author: David Dos Santos Ferreira,Wolfgang Staubach
Publisher: American Mathematical Soc.
ISBN: 0821891197
Category: Mathematics
Page: 65
View: 2238
The authors investigate the global continuity on spaces with of Fourier integral operators with smooth and rough amplitudes and/or phase functions subject to certain necessary non-degeneracy conditions. In this context they prove the optimal global boundedness result for Fourier integral operators with non-degenerate phase functions and the most general smooth Hörmander class amplitudes i.e. those in with . They also prove the very first results concerning the continuity of smooth and rough Fourier integral operators on weighted spaces, with and (i.e. the Muckenhoupt weights) for operators with rough and smooth amplitudes and phase functions satisfying a suitable rank condition.


    • Mathematics

Fourier Integral Operators


Author: Johannes Jisse Duistermaat
Publisher: Springer Science & Business Media
ISBN: 9780817638214
Category: Mathematics
Page: 142
View: 544
This volume serves as an introduction to the subject of Fourier integral operators. Covering a range of topics from Hormander's exposition of the theory, Duistermaat approaches the subject of symplectic geometry, and includes applications to hyperbolic equations (equations of wave type).




    • Mathematics

The Analysis of Linear Partial Differential Operators IV

Fourier Integral Operators
Author: Lars Hörmander
Publisher: Springer Science & Business Media
ISBN: 9783642001369
Category: Mathematics
Page: 352
View: 4060
From the reviews: "Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators." L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987 "This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation." J. Brüning in Zentralblatt MATH, 1987 Honours awarded to Lars Hörmander: Fields Medal 1962, Speaker at International Congress 1970, Wolf Prize 1988, AMS Steele Prize 2006

    • Mathematics

Nonlinear Integral Operators and Applications


Author: Carlo Bardaro,Julian Musielak,Gianluca Vinti
Publisher: Walter de Gruyter
ISBN: 9783110175516
Category: Mathematics
Page: 201
View: 3843
This volume presents a comprehensive treatment of approximation theory by means of nonlinear integral operator in function spaces. In particular, the fundamental notions of approximate identity for kernels of nonlinear operators and a general concept of modulus of continuity are developed.