Fourier Integral Operators and Partial Differential Equations
Author : J. Chazarain
Publisher :
Page : 384 pages
File Size : 49,25 MB
Release : 2014-01-15
Category :
ISBN : 9783662180938
Author : J. Chazarain
Publisher :
Page : 384 pages
File Size : 49,25 MB
Release : 2014-01-15
Category :
ISBN : 9783662180938
Author : J. Chazarain
Publisher : Springer
Page : 383 pages
File Size : 27,81 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 354037521X
Author : Lars Hörmander
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 37,9 MB
Release : 2009-04-28
Category : Mathematics
ISBN : 364200136X
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
Author : J CHAZARAIN (ED.)
Publisher :
Page : pages
File Size : 44,38 MB
Release : 1975
Category :
ISBN :
Author : Lars Hörmander
Publisher : Springer
Page : 376 pages
File Size : 10,20 MB
Release : 1994-12-16
Category : Mathematics
ISBN : 9783540138297
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
Author :
Publisher :
Page : 372 pages
File Size : 36,6 MB
Release : 1964
Category : Differential equations, Partial
ISBN : 9780387071800
Author : J.J. Duistermaat
Publisher : Springer Science & Business Media
Page : 155 pages
File Size : 47,74 MB
Release : 2010-11-03
Category : Mathematics
ISBN : 0817681086
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.
Author : Jean-François Treves
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 31,92 MB
Release : 2013-12-11
Category : Mathematics
ISBN : 1468487809
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.
Author : Yu.V. Egorov
Publisher : Springer Science & Business Media
Page : 269 pages
File Size : 12,50 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 3642578764
This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.
Author : Jose Garcia-Cuerva
Publisher : CRC Press
Page : 432 pages
File Size : 30,71 MB
Release : 2018-01-18
Category : Mathematics
ISBN : 135108903X
Fourier Analysis and Partial Differential Equations presents the proceedings of the conference held at Miraflores de la Sierra in June 1992. These conferences are held periodically to assess new developments and results in the field. The proceedings are divided into two parts. Four mini-courses present a rich and actual piece of mathematics assuming minimal background from the audience and reaching the frontiers of present-day research. Twenty lectures cover a wide range of data in the fields of Fourier analysis and PDE. This book, representing the fourth conference in the series, is dedicated to the late mathematician Antoni Zygmund, who founded the Chicago School of Fourier Analysis, which had a notable influence in the development of the field and significantly contributed to the flourishing of Fourier analysis in Spain.