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Author: Alain Grigis
Publisher: Cambridge University Press
Published: 1994-03-03
Total Pages: 164
ISBN-13: 9780521449861
DOWNLOAD EBOOKThis book corresponds to a graduate course given many times by the authors, and should prove to be useful to mathematicians and theoretical physicists.
Author: Alain Grigis
Publisher:
Published: 2014-02-19
Total Pages:
ISBN-13: 9781299748866
DOWNLOAD EBOOKThis book corresponds to a graduate course given many times by the authors, and should prove to be useful to mathematicians and theoretical physicists.
Author: Victor Ivrii
Publisher: Springer Science & Business Media
Published: 1998-05-20
Total Pages: 756
ISBN-13: 9783540627807
DOWNLOAD EBOOKThis long awaited book is devoted to the methods of microlocal semiclassical analysis in application to spectral asymptotics with accurate remainder estimates. The very powerful machinery of local and microlocal semiclassical spectral asymptotics is developed as well as methods in combining these asymptotics with spectral estimates. The rescaling technique should be mentioned as an easy as to use and very powerful tool. Many theorems, considered before as independent and difficult, now are just special cases of easy corollaries of the theorems proved in the book. Most of the results and almost all the proofs are as yet unpublished
Author: Maciej Zworski
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 448
ISBN-13: 0821883208
DOWNLOAD EBOOK"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.
Author: Xavier Saint Raymond
Publisher: Routledge
Published: 2018-02-06
Total Pages: 120
ISBN-13: 1351452932
DOWNLOAD EBOOKIn the 19th century, the Fourier transformation was introduced to study various problems of partial differential equations. Since 1960, this old tool has been developed into a well-organized theory called microlocal analysis that is based on the concept of the pseudo-differential operator. This book provides the fundamental knowledge non-specialists need in order to use microlocal analysis. It is strictly mathematical in the sense that it contains precise definitions, statements of theorems and complete proofs, and follows the usual method of pure mathematics. The book explains the origin of the theory (i.e., Fourier transformation), presents an elementary construcion of distribution theory, and features a careful exposition of standard pseudodifferential theory. Exercises, historical notes, and bibliographical references are included to round out this essential book for mathematics students; engineers, physicists, and mathematicians who use partial differential equations; and advanced mathematics instructors.
Author: André Bach
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 193
ISBN-13: 1475744951
DOWNLOAD EBOOKThis book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical, way and is mainly addressed to non-specialists in the subject. It is based on lectures taught by the author over several years, and includes many exercises providing outlines of useful applications of the semi-classical theory.
Author: Serge Alinhac
Publisher: American Mathematical Soc.
Published: 2007
Total Pages: 178
ISBN-13: 0821834541
DOWNLOAD EBOOKThis book presents two essential and apparently unrelated subjects. The first, microlocal analysis and the theory of pseudo-differential operators, is a basic tool in the study of partial differential equations and in analysis on manifolds. The second, the Nash-Moser theorem, continues to be fundamentally important in geometry, dynamical systems and nonlinear PDE. Each of the subjects, which are of interest in their own right as well as for applications, can be learned separately. But the book shows the deep connections between the two themes, particularly in the middle part, which is devoted to Littlewood-Paley theory, dyadic analysis, and the paradifferential calculus and its application to interpolation inequalities. An important feature is the elementary and self-contained character of the text, to which many exercises and an introductory Chapter $0$ with basic material have been added. This makes the book readable by graduate students or researchers from one subject who are interested in becoming familiar with the other. It can also be used as a textbook for a graduate course on nonlinear PDE or geometry.
Author: Michael Eugene Taylor
Publisher: American Mathematical Soc.
Published: 1984
Total Pages: 188
ISBN-13: 0821823140
DOWNLOAD EBOOKAuthor: Nicolas Lerner
Publisher: Springer Science & Business Media
Published: 2011-01-30
Total Pages: 408
ISBN-13: 3764385103
DOWNLOAD EBOOKThis book is devoted to the study of pseudo-di?erential operators, with special emphasis on non-selfadjoint operators, a priori estimates and localization in the phase space. We have tried here to expose the most recent developments of the theory with its applications to local solvability and semi-classical estimates for non-selfadjoint operators. The?rstchapter,Basic Notions of Phase Space Analysis,isintroductoryand gives a presentation of very classical classes of pseudo-di?erential operators, along with some basic properties. As an illustration of the power of these methods, we give a proof of propagation of singularities for real-principal type operators (using aprioriestimates,andnotFourierintegraloperators),andweintroducethereader to local solvability problems. That chapter should be useful for a reader, say at the graduate level in analysis, eager to learn some basics on pseudo-di?erential operators. The second chapter, Metrics on the Phase Space begins with a review of symplectic algebra, Wigner functions, quantization formulas, metaplectic group and is intended to set the basic study of the phase space. We move forward to the more general setting of metrics on the phase space, following essentially the basic assumptions of L. H ̀ˆ ormander (Chapter 18 in the book [73]) on this topic.
Author: M.A. Shubin
Publisher: Springer Science & Business Media
Published: 2011-06-28
Total Pages: 296
ISBN-13: 3642565794
DOWNLOAD EBOOKI had mixed feelings when I thought how I should prepare the book for the second edition. It was clear to me that I had to correct all mistakes and misprints that were found in the book during the life of the first edition. This was easy to do because the mistakes were mostly minor and easy to correct, and the misprints were not many. It was more difficult to decide whether I should update the book (or at least its bibliography) somehow. I decided that it did not need much of an updating. The main value of any good mathematical book is that it teaches its reader some language and some skills. It can not exhaust any substantial topic no matter how hard the author tried. Pseudodifferential operators became a language and a tool of analysis of partial differential equations long ago. Therefore it is meaningless to try to exhaust this topic. Here is an easy proof. As of July 3, 2000, MathSciNet (the database of the American Mathematical Society) in a few seconds found 3695 sources, among them 363 books, during its search for "pseudodifferential operator". (The search also led to finding 963 sources for "pseudo-differential operator" but I was unable to check how much the results ofthese two searches intersected). This means that the corresponding words appear either in the title or in the review published in Mathematical Reviews.
