Download or read book Introduction to Pseudodifferential and Fourier Integral Operators written by Jean-François Treves and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Pseudodifferential and Fourier Integral Operators written by François Treves and published by . This book was released on 1982 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction To Pseudo differential Operators An 3rd Edition written by Man-wah Wong and published by World Scientific Publishing Company. This book was released on 2014-03-11 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Pseudodifferential and Fourier Integral Operators Volume 2 written by François Trèves and published by Springer Science & Business Media. This book was released on 1980 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elementary Introduction to the Theory of Pseudodifferential Operators written by Xavier Saint Raymond and published by Routledge. This book was released on 2018-02-06 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Pseudodifferential and Fourier Integral Operators written by François Treves and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Pseudodifferential and Fourier Integral Operators written by Francois Treves and published by Springer. This book was released on 1980-11-30 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Elementary Introduction to the Theory of Pseudodifferential Operators written by Xavier Saint Raymond and published by Routledge. This book was released on 2018-02-06 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Pseudodifferential and Fourier Integral Operators written by François Treves and published by . This book was released on 1982 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete Fourier Analysis written by M. W. Wong and published by Springer Science & Business Media. This book was released on 2011-05-30 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis. The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis. Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.
Download or read book Introduction to the Fourier Transform Pseudo differential Operators written by Bent E. Petersen and published by Pitman Advanced Publishing Program. This book was released on 1983 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Pseudodifferential and Fourier written by Francois Treves and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pseudodifferential and Singular Integral Operators written by Helmut Abels and published by Walter de Gruyter. This book was released on 2011-12-23 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Elementary Introduction to the Theory of Pseudodifferential Operators written by Xavier Saint Raymond and published by CRC Press. This book was released on 1991-09-17 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Boundary Integral Equations written by George C. Hsiao and published by Springer Nature. This book was released on 2021-03-26 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of the book which has two additional new chapters on Maxwell’s equations as well as a section on properties of solution spaces of Maxwell’s equations and their trace spaces. These two new chapters, which summarize the most up-to-date results in the literature for the Maxwell’s equations, are sufficient enough to serve as a self-contained introductory book on the modern mathematical theory of boundary integral equations in electromagnetics. The book now contains 12 chapters and is divided into two parts. The first six chapters present modern mathematical theory of boundary integral equations that arise in fundamental problems in continuum mechanics and electromagnetics based on the approach of variational formulations of the equations. The second six chapters present an introduction to basic classical theory of the pseudo-differential operators. The aforementioned corresponding boundary integral operators can now be recast as pseudo-differential operators. These serve as concrete examples that illustrate the basic ideas of how one may apply the theory of pseudo-differential operators and their calculus to obtain additional properties for the corresponding boundary integral operators. These two different approaches are complementary to each other. Both serve as the mathematical foundation of the boundary element methods, which have become extremely popular and efficient computational tools for boundary problems in applications. This book contains a wide spectrum of boundary integral equations arising in fundamental problems in continuum mechanics and electromagnetics. The book is a major scholarly contribution to the modern approaches of boundary integral equations, and should be accessible and useful to a large community of advanced graduate students and researchers in mathematics, physics, and engineering.
Download or read book An Introduction to Pseudo differential Operators written by Man Wah Wong and published by World Scientific. This book was released on 1999 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Pseudo Differential Operators and Symmetries written by Michael Ruzhansky and published by Springer Science & Business Media. This book was released on 2009-12-29 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
