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Author : J. Chazarain
Publisher : Springer
Page : 383 pages
File Size : 51,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540375210
Author : J. Chazarain
Publisher : Unknown
Page : 384 pages
File Size : 50,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662180936
Author : Lars Hörmander
Publisher : Unknown
Page : 376 pages
File Size : 50,5 Mb
Release : 1983
Category : Differential equations, Partial
ISBN : UCSD:31822001094333
Author : Lars Hörmander
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 47,5 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9783642001369
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 : Anonim
Publisher : Unknown
Page : 372 pages
File Size : 41,9 Mb
Release : 1964
Category : Differential equations, Partial
ISBN : 0387071806
Author : Jean-François Treves
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 40,6 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781468487800
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 : J.J. Duistermaat
Publisher : Springer Science & Business Media
Page : 142 pages
File Size : 43,7 Mb
Release : 2010-11-03
Category : Mathematics
ISBN : 9780817681081
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 : Yu.V. Egorov,A.I. Komech,M.A. Shubin
Publisher : Springer Science & Business Media
Page : 269 pages
File Size : 48,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642578762
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 : François Trèves,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 50,9 Mb
Release : 1985
Category : Mathematics
ISBN : 9780821814697
"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.
Author : Luigi Rodino
Publisher : World Scientific
Page : 266 pages
File Size : 55,9 Mb
Release : 1993-03-30
Category : Mathematics
ISBN : 9789814505871
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.
Author : George F. Oster,Edward O. Wilson
Publisher : Princeton University Press
Page : 295 pages
File Size : 53,5 Mb
Release : 1978
Category : Mathematics
ISBN : 9780691082134
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.
Author : Heinrich Begehr,R.P. Gilbert,Wen-Chung Guo
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 48,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461332763
This volume of the Proceedings of the congress ISAAC '97 collects the con tributions of the four sections 1. Function theoretic and functional analytic methods for pde, 2. Applications of function theory of several complex variables to pde, 3. Integral equations and boundary value problems, 4. Partial differential equations. Most but not all of the authors have participated in the congress. Unfortunately some from Eastern Europe and Asia have not managed to come because of lack of financial support. Nevertheless their manuscripts of the proposed talks are included in this volume. The majority of the papers deal with complex methods. Among them boundary value problems in particular the Riemann-Hilbert, the Riemann (Hilbert) and related problems are treated. Boundary behaviour of vector-valued functions are studied too. The Riemann-Hilbert problem is solved for elliptic complex equations, for mixed complex equations, and for several complex variables. It is considered in a general topological setting for mappings into q;n and related to Toeplitz operators. Convolution operators are investigated for nilpotent Lie groups leading to some consequences for the null space of the tangential Cauchy Riemann operator. Some boundary value problems for overdetermined systems in balls of q;n are solved explicitly. A survey is given for the Gauss-Manin connection associated with deformations of curve singularities. Several papers deal with generalizations of analytic functions with various applications to mathematical physics. Singular integrals in quaternionic anal ysis are studied which are applied to the time-harmonic Maxwell equations.
Author : Jean-François Treves
Publisher : Springer
Page : 299 pages
File Size : 40,6 Mb
Release : 1980-11-30
Category : Mathematics
ISBN : 0306404036
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 : G. Buttazzo,Giselle Galdi,L. Zanghirati
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461530329
During the days 14-18 of October 1991, we had the pleasure of attending a most interesting Conference on New Developments in Partial Differential Equations and Applications to Mathematical Physics in Ferrarra. The Conference was organized within the Scientific Program celebrating the six hundredth birthday of the University of Ferrarra and, after the many stimulating lectures and fruitful discussions, we may certainly conclude, together with the numerous participants, that it has represented a big success. The Conference would not have been possible without the financial support of several sources. In this respect, we are particularly grateful to the Comitato Organizzatore del VI Centenario, the University of Ferrarra in the Office of the Rector, Professor Antonio Rossi, the Consiglio Nationale delle Ricerche, and the Department of Mathematics of the University of Ferrarra. We should like to thank all of the partlClpants and the speakers, and we are especially grateful to those who have contributed to the present volume. G. Buttazzo, University of Pisa G.P. Galdi, University of Ferrarra L. Zanghirati, University of Ferrarra Ferrarra, May 11 th, 1992 v CONTENTS INVITED LECTURES Liapunov Functionals and Qualitative Behaviour of the Solution to the Nonlinear Enskog Equation ...
Author : Lars Hörmander
Publisher : Springer
Page : 454 pages
File Size : 53,5 Mb
Release : 2015-03-30
Category : Mathematics
ISBN : 9783642614972
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.