Pseudodifferential Operators With Applications

Author : Helmut Abels
Publisher : Walter de Gruyter
Page : 233 pages
File Size : 46,5 Mb
Release : 2011-12-23
Category : Mathematics
ISBN : 9783110250312

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Pseudodifferential and Singular Integral Operators by Helmut Abels Pdf

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 : François Trèves,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 50,9 Mb
Release : 1985
Category : Mathematics
ISBN : 9780821814697

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Pseudodifferential Operators and Applications by François Trèves,American Mathematical Society Pdf

"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 : Alexander Nagel,Elias M. Stein
Publisher : Princeton University Press
Page : 167 pages
File Size : 47,5 Mb
Release : 2015-03-08
Category : Mathematics
ISBN : 9781400870486

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Lectures on Pseudo-Differential Operators by Alexander Nagel,Elias M. Stein Pdf

The theory of pseudo-differential operators (which originated as singular integral operators) was largely influenced by its application to function theory in one complex variable and regularity properties of solutions of elliptic partial differential equations. Given here is an exposition of some new classes of pseudo-differential operators relevant to several complex variables and certain non-elliptic problems. Originally published in 1979. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : A. Avantaggiati
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 45,5 Mb
Release : 2011-06-07
Category : Mathematics
ISBN : 9783642110924

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Pseudodifferential Operators with Applications by A. Avantaggiati Pdf

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 : A. Avantaggiati
Publisher : Unknown
Page : 250 pages
File Size : 55,5 Mb
Release : 2011-03-30
Category : Electronic
ISBN : 3642110932

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Pseudodifferential Operators with Applications by A. Avantaggiati Pdf

Author : M W Wong
Publisher : World Scientific Publishing Company
Page : 196 pages
File Size : 47,8 Mb
Release : 2014-03-11
Category : Mathematics
ISBN : 9789814583107

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An Introduction to Pseudo-Differential Operators by M W Wong Pdf

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 : Michael Ruzhansky,Ville Turunen
Publisher : Springer Science & Business Media
Page : 712 pages
File Size : 55,9 Mb
Release : 2009-12-29
Category : Mathematics
ISBN : 9783764385149

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Pseudo-Differential Operators and Symmetries by Michael Ruzhansky,Ville Turunen Pdf

This monograph is devoted to the development of the theory of pseudo-di?erential n operators on spaces with symmetries. Such spaces are the Euclidean space R ,the n torus T , compact Lie groups and compact homogeneous spaces. The book consists of several parts. One of our aims has been not only to present new results on pseudo-di?erential operators but also to show parallels between di?erent approaches to pseudo-di?erential operators on di?erent spaces. Moreover, we tried to present the material in a self-contained way to make it accessible for readers approaching the material for the ?rst time. However, di?erent spaces on which we develop the theory of pseudo-di?er- tial operators require di?erent backgrounds. Thus, while operators on the - clidean space in Chapter 2 rely on the well-known Euclidean Fourier analysis, pseudo-di?erentialoperatorsonthetorusandmoregeneralLiegroupsinChapters 4 and 10 require certain backgrounds in discrete analysis and in the representation theory of compact Lie groups, which we therefore present in Chapter 3 and in Part III,respectively. Moreover,anyonewhowishestoworkwithpseudo-di?erential- erators on Lie groups will certainly bene?t from a good grasp of certain aspects of representation theory. That is why we present the main elements of this theory in Part III, thus eliminating the necessity for the reader to consult other sources for most of the time. Similarly, the backgrounds for the theory of pseudo-di?erential 3 operators on S and SU(2) developed in Chapter 12 can be found in Chapter 11 presented in a self-contained way suitable for immediate use.

Author : I͡Uriĭ Vladimirovich Egorov
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 54,7 Mb
Release : 1997
Category : Fourier integral operators
ISBN : 3764354844

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Pseudo-Differential Operators, Singularities, Applications by I͡Uriĭ Vladimirovich Egorov Pdf

Author : Michael E. Taylor
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 55,7 Mb
Release : 2000
Category : Differential equations, Partial
ISBN : 9780821843789

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Tools for PDE by Michael E. Taylor Pdf

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 : Xavier Saint Raymond
Publisher : Routledge
Page : 71 pages
File Size : 54,9 Mb
Release : 2018-02-06
Category : Mathematics
ISBN : 9781351452922

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Elementary Introduction to the Theory of Pseudodifferential Operators by Xavier Saint Raymond Pdf

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 : Bert-Wolfgang Schulze,M. W. Wong
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 47,6 Mb
Release : 2010-03-01
Category : Mathematics
ISBN : 9783034601986

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Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations by Bert-Wolfgang Schulze,M. W. Wong Pdf

Consists of the expository paper based on the 6-hour minicourse given by Professor Bert-Wolfgang Schulze, and sixteen papers based on lectures given at the workshop and on invitations.

Author : Serge Alinhac,Patrick Gérard
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 54,7 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821834541

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Pseudo-differential Operators and the Nash-Moser Theorem by Serge Alinhac,Patrick Gérard Pdf

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.

Author : M.A. Shubin
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 54,5 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9783642565793

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Pseudodifferential Operators and Spectral Theory by M.A. Shubin Pdf

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 : Heinz Otto Cordes
Publisher : Cambridge University Press
Page : 398 pages
File Size : 44,8 Mb
Release : 1995-02-23
Category : Mathematics
ISBN : 9780521378642

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The Technique of Pseudodifferential Operators by Heinz Otto Cordes Pdf

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 : M. W. Wong,Hongmei Zhu
Publisher : Birkhäuser
Page : 239 pages
File Size : 54,6 Mb
Release : 2017-01-20
Category : Mathematics
ISBN : 9783319475127

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Pseudo-Differential Operators: Groups, Geometry and Applications by M. W. Wong,Hongmei Zhu Pdf

This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.