Pseudodifferential Operators With Applications
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| Author | : Helmut Abels |
| Publisher | : Walter de Gruyter |
| Total Pages | : 233 |
| Release | : 2011-12-23 |
| Genre | : Mathematics |
| ISBN | : 3110250314 |
Download Pseudodifferential and Singular Integral Operators Book in PDF, Epub and Kindle
This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. In the first chapters, the necessary material on Fourier transformation and distribution theory is presented. Subsequently the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space is developed. In order to present the deep results on regularity questions for partial differential equations, an introduction to the theory of singular integral operators is given - which is of interest for its own. Moreover, to get a wide range of applications, one chapter is devoted to the modern theory of Besov and Bessel potential spaces. In order to demonstrate some fundamental approaches and the power of the theory, several applications to wellposedness and regularity question for elliptic and parabolic equations are presented throughout the book. The basic notation of functional analysis needed in the book is introduced and summarized in the appendix. The text is comprehensible for students of mathematics and physics with a basic education in analysis.
| Author | : A. Avantaggiati |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 238 |
| Release | : 2011-06-07 |
| Genre | : Mathematics |
| ISBN | : 3642110924 |
Download Pseudodifferential Operators with Applications Book in PDF, Epub and Kindle
A. Dynin: Pseudo-differential operators on Heisenberg groups.- A. Dynin: An index formula for elliptic boundary problems.- G.I. Eskin: General mixed boundary problems for elliptic differential equations.- B. Helffer: Hypoellipticité pour des opérateurs différentiels sur des groupes de Lie nilpotents.- J.J. Kohn: Lectures on degenerate elliptic problems.- K. Taira: Conditions nécessaires et suffisantes pour l’existence et l’unicité des solutions du problème de la dérivée oblique.- F. Treves: Boundary value problems for elliptic equations.
| Author | : Man-wah Wong |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 195 |
| Release | : 2014-03-11 |
| Genre | : Mathematics |
| ISBN | : 9814583103 |
Download Introduction To Pseudo-differential Operators, An (3rd Edition) Book in PDF, Epub and Kindle
The aim of this third edition is to give an accessible and essentially self-contained account of pseudo-differential operators based on the previous edition. New chapters notwithstanding, the elementary and detailed style of earlier editions is maintained in order to appeal to the largest possible group of readers. The focus of this book is on the global theory of elliptic pseudo-differential operators on Lp(Rn).The main prerequisite for a complete understanding of the book is a basic course in functional analysis up to the level of compact operators. It is an ideal introduction for graduate students in mathematics and mathematicians who aspire to do research in pseudo-differential operators and related topics.
| Author | : Francois Treves |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 311 |
| Release | : 1985 |
| Genre | : Mathematics |
| ISBN | : 0821814699 |
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"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 | : Xavier Saint Raymond |
| Publisher | : Routledge |
| Total Pages | : 120 |
| Release | : 2018-02-06 |
| Genre | : Mathematics |
| ISBN | : 1351452932 |
Download Elementary Introduction to the Theory of Pseudodifferential Operators Book in PDF, Epub and Kindle
In 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 | : M.A. Shubin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 296 |
| Release | : 2011-06-28 |
| Genre | : Mathematics |
| ISBN | : 3642565794 |
Download Pseudodifferential Operators and Spectral Theory Book in PDF, Epub and Kindle
I 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.
| Author | : A. Avantaggiati |
| Publisher | : |
| Total Pages | : 250 |
| Release | : 2011-03-30 |
| Genre | : |
| ISBN | : 9783642110931 |
Download Pseudodifferential Operators with Applications Book in PDF, Epub and Kindle
| Author | : Michael E. Taylor |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 274 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821843788 |
Download Tools for PDE Book in PDF, Epub and Kindle
Developing three related tools that are useful in the analysis of partial differential equations (PDEs) arising from the classical study of singular integral operators, this text considers pseudodifferential operators, paradifferential operators, and layer potentials.
| Author | : Heinz Otto Cordes |
| Publisher | : Cambridge University Press |
| Total Pages | : 398 |
| Release | : 1995-02-23 |
| Genre | : Mathematics |
| ISBN | : 0521378648 |
Download The Technique of Pseudodifferential Operators Book in PDF, Epub and Kindle
Pseudodifferential operators arise naturally in a solution of boundary problems for partial differential equations. The formalism of these operators serves to make the Fourier-Laplace method applicable for nonconstant coefficient equations. This book presents the technique of pseudodifferential operators and its applications, especially to the Dirac theory of quantum mechanics. The treatment uses 'Leibniz formulas' with integral remainders or as asymptotic series. While a pseudodifferential operator is commonly defined by an integral formula, it also may be described by invariance under action of a Lie group. The author discusses connections to the theory of C*-algebras, invariant algebras of pseudodifferential operators under hyperbolic evolution, and the relation of the hyperbolic theory to the propagation of maximal ideals. The Technique of Pseudodifferential Operators will be of particular interest to researchers in partial differential equations and mathematical physics.
| Author | : Serge Alinhac |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 178 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821834541 |
Download Pseudo-differential Operators and the Nash-Moser Theorem Book in PDF, Epub and Kindle
This 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.
