Download or read book Fourier Integral Operators and Partial Differential Equations written by J. Chazarain and published by Springer. This book was released on 2006-11-14 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fourier Integral Operators and Partial Differential Equations written by J. Chazarain and published by . This book was released on 2014-01-15 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Analysis of Linear Partial Differential Operators written by Lars Hörmander and published by . This book was released on 1983 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fourier Integral Operators written by J.J. Duistermaat and published by Springer Science & Business Media. This book was released on 2010-11-03 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lecture Notes in Mathematics written by and published by . This book was released on 1964 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Analysis of Linear Partial Differential Operators IV written by Lars Hörmander and published by Springer Science & Business Media. This book was released on 2009-04-28 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Introduction to Pseudodifferential and Fourier Integral Operators written by Jean-François Treves and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Pseudodifferential Operators and Applications written by Francois Treves and published by American Mathematical Soc.. This book was released on 1985 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Proceedings of the Symposium on Pseudodifferential Operators and Fourier Integral Operators with Applications to Partial Differential Equations held at the University of Notre Dame, Notre Dame, Indiana, April 2-5, 1984"--T.p. verso.
Download or read book Introduction to Pseudodifferential and Fourier Integral Operators written by François Treves and published by . This book was released on 1982 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Partial Differential Equations II written by Yu.V. Egorov and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Pseudodifferential and Fourier Integral Operators written by Jean-François Treves and published by Springer. This book was released on 1980-11-30 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Seminar on Singularities of Solutions of Linear Partial Differential Equations written by George F. Oster and published by Princeton University Press. This book was released on 1978 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularities of solutions of differential equations forms the common theme of these papers taken from a seminar held at the Institute for Advanced Study in Princeton in 1977-1978. While some of the lectures were devoted to the analysis of singularities, others focused on applications in spectral theory. As an introduction to the subject, this volume treats current research in the field in such a way that it can be studied with profit by the non-specialist.
Download or read book Linear Partial Differential Operators In Gevrey Spaces written by Luigi Rodino and published by World Scientific. This book was released on 1993-03-30 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to new and classical results of the theory of linear partial differential operators in Gevrey spaces. The “microlocal approach” is adopted, by using pseudo-differential operators, wave front sets and Fourier integral operators.Basic results for Schwartz-distributions, c∞ and analytic classes are also included, concerning hypoellipticity, solvability and propagation of singularities.Also included is a self-contained exposition of the calculus of the pseudo-differential operators of infinite order.
Download or read book Fourier Analysis and Partial Differential Equations written by Jose Garcia-Cuerva and published by CRC Press. This book was released on 2018-01-18 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fourier Integrals in Classical Analysis written by Christopher D. Sogge and published by Cambridge University Press. This book was released on 2017-04-27 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents Hörmander's propagation of singularities theorem and uses this to prove the Duistermaat-Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff.
Download or read book L p Boundedness of Fourier Integral Operators written by Michael Beals and published by American Mathematical Soc.. This book was released on 1982 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Analysis of Linear Partial Differential Operators I written by Lars Hörmander and published by Springer. This book was released on 2015-03-30 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration.
