Elementary Introduction To The Theory Of Pseudodifferential Operators

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Elementary Introduction to the Theory of Pseudodifferential Operators

Xavier Saint Raymond
Elementary Introduction to the Theory of Pseudodifferential Operators Book PDF

Author : Xavier Saint Raymond
Publisher : Routledge
Page : 71 pages
File Size : 41,5 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.

Elementary Introduction to the Theory of Pseudodifferential Operators

Xavier Saint Raymond
Elementary Introduction to the Theory of Pseudodifferential Operators Book PDF

Author : Xavier Saint Raymond
Publisher : Routledge
Page : 120 pages
File Size : 40,7 Mb
Release : 2018-02-06
Category : Mathematics
ISBN : 9781351452939

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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.

An Introduction to Pseudo-Differential Operators

M W Wong
An Introduction to Pseudo Differential Operators Book PDF

Author : M W Wong
Publisher : World Scientific Publishing Company
Page : 196 pages
File Size : 44,5 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.

Pseudodifferential and Singular Integral Operators

Helmut Abels
Pseudodifferential and Singular Integral Operators Book PDF

Author : Helmut Abels
Publisher : Walter de Gruyter
Page : 233 pages
File Size : 40,5 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.

Pseudo-Differential Operators and Symmetries

Michael Ruzhansky,Ville Turunen
Pseudo Differential Operators and Symmetries Book PDF

Author : Michael Ruzhansky,Ville Turunen
Publisher : Springer Science & Business Media
Page : 710 pages
File Size : 41,6 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.

Pseudo-differential Operators and the Nash-Moser Theorem

Serge Alinhac,Patrick Gérard
Pseudo differential Operators and the Nash Moser Theorem Book PDF

Author : Serge Alinhac,Patrick Gérard
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 46,7 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.

An Introduction to Pseudo-differential Operators

Man Wah Wong
An Introduction to Pseudo differential Operators Book PDF

Author : Man Wah Wong
Publisher : World Scientific
Page : 156 pages
File Size : 46,5 Mb
Release : 1999
Category : Mathematics
ISBN : 9810238134

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An Introduction to Pseudo-differential Operators by Man Wah Wong Pdf

In this new edition of An Introduction to Pseudo-Differential Operators, the style & scope of the original book are retained. A chapter on the interchange of order of differentiation & integration is added at the beginning to make the book more self-contained, & a chapter on weak solutions of pseudo-differential equations is added at the end to enhance the value of the book as a work on partial differential equations. Several chapters are provided with additional exercises. The bibliography is slightly expanded & an index is added. Contents: Differentiation of Integrals Depending on Parameters; The Convolution; The Fourier Transform; Tempered Distributions; Symbols, Pseudo-Differential Operators & Asymptotic Expansions; A Partition of Unity & Taylor's Formula; The Product of Two Pseudo-Differential Operators; The Formal Adjoint of a Pseudo-Differential Operator; The Parametrix of an Elliptic Pseudo-Differential Operator; Lp-Boundedness of Pseudo-Differential Operators, 1

Introduction To Pseudo-differential Operators, An (2nd Edition)

Man-wah Wong
Introduction To Pseudo differential Operators An 2nd Edition Book PDF

Author : Man-wah Wong
Publisher : World Scientific Publishing Company
Page : 150 pages
File Size : 41,7 Mb
Release : 1999-04-29
Category : Mathematics
ISBN : 9789813105423

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Introduction To Pseudo-differential Operators, An (2nd Edition) by Man-wah Wong Pdf

In this new edition of An Introduction to Pseudo-Differential Operators, the style and scope of the original book are retained. A chapter on the interchange of order of differentiation and integration is added at the beginning to make the book more self-contained, and a chapter on weak solutions of pseudo-differential equations is added at the end to enhance the value of the book as a work on partial differential equations. Several chapters are provided with additional exercises. The bibliography is slightly expanded and an index is added.

Methods of Noncommutative Analysis

Vladimir E. Nazaikinskii,Victor E. Shatalov,Boris Yu. Sternin
Methods of Noncommutative Analysis Book PDF

Author : Vladimir E. Nazaikinskii,Victor E. Shatalov,Boris Yu. Sternin
Publisher : Walter de Gruyter
Page : 385 pages
File Size : 41,5 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110813548

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Methods of Noncommutative Analysis by Vladimir E. Nazaikinskii,Victor E. Shatalov,Boris Yu. Sternin Pdf

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic Models for Fractional Calculus, second edition (2018) Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Kezheng Li, Group Schemes and Their Actions (2019; together with Tsinghua University Press) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

Distributions and Operators

Gerd Grubb
Distributions and Operators Book PDF

Author : Gerd Grubb
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 49,6 Mb
Release : 2008-10-14
Category : Mathematics
ISBN : 9780387848945

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Distributions and Operators by Gerd Grubb Pdf

This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. It is the first book to present distribution theory as a standard text. Each chapter has been enhanced with many exercises and examples.

Solvable Algebras of Pseudodifferential Operators

Boris Plamenevskii,Oleg Sarafanov
Solvable Algebras of Pseudodifferential Operators Book PDF

Author : Boris Plamenevskii,Oleg Sarafanov
Publisher : Springer Nature
Page : 249 pages
File Size : 42,7 Mb
Release : 2023-05-04
Category : Mathematics
ISBN : 9783031283987

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Solvable Algebras of Pseudodifferential Operators by Boris Plamenevskii,Oleg Sarafanov Pdf

This book presents original research results on pseudodifferential operators. C*-algebras generated by pseudodifferential operators with piecewise smooth symbols on a smooth manifold are considered. For each algebra, all the equivalence classes of irreducible representations are listed; as a consequence, a criterion for a pseudodifferential operator to be Fredholm is stated, the topology on the spectrum is described, and a solving series is constructed. Pseudodifferential operators on manifolds with edges are introduced, their properties are considered in details, and an algebra generated by the operators is studied. An introductory chapter includes all necessary preliminaries from the theory of pseudodifferential operators and C*-algebras.

Pseudo-Differential Operators and Symmetries

Michael V. Ruzhansky,Ville Turunen
Pseudo Differential Operators and Symmetries Book PDF

Author : Michael V. Ruzhansky,Ville Turunen
Publisher : Springer Science & Business Media
Page : 712 pages
File Size : 52,5 Mb
Release : 2009-10-19
Category : Mathematics
ISBN : 9783764385132

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Pseudo-Differential Operators and Symmetries by Michael V. 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.

Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators

Nicolas Lerner
Metrics on the Phase Space and Non Selfadjoint Pseudo Differential Operators Book PDF

Author : Nicolas Lerner
Publisher : Springer Science & Business Media
Page : 397 pages
File Size : 44,6 Mb
Release : 2011-01-30
Category : Mathematics
ISBN : 9783764385101

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Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators by Nicolas Lerner Pdf

This 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 ̈ ormander (Chapter 18 in the book [73]) on this topic.

Pseudo-Differential Operators

Hans G. Feichtinger,Bernard Helffer,Michael Lamoureux,Nicolas Lerner,Joachim Toft
Pseudo Differential Operators Book PDF

Author : Hans G. Feichtinger,Bernard Helffer,Michael Lamoureux,Nicolas Lerner,Joachim Toft
Publisher : Springer
Page : 214 pages
File Size : 50,5 Mb
Release : 2008-08-15
Category : Mathematics
ISBN : 9783540682684

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Pseudo-Differential Operators by Hans G. Feichtinger,Bernard Helffer,Michael Lamoureux,Nicolas Lerner,Joachim Toft Pdf

Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.

New Developments in Pseudo-Differential Operators

Luigi Rodino,M. W. Wong
New Developments in Pseudo Differential Operators Book PDF

Author : Luigi Rodino,M. W. Wong
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 51,9 Mb
Release : 2009-01-06
Category : Mathematics
ISBN : 9783764389697

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New Developments in Pseudo-Differential Operators by Luigi Rodino,M. W. Wong Pdf

This volume consists of peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held on August 13-18, 2007, and invited papers by experts in the field.