Introduction To Pseudo-differential Operators, An (3rd Edition) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction To Pseudo-differential Operators, An (3rd Edition) write by Man-wah Wong. This book was released on 2014-03-11. Introduction To Pseudo-differential Operators, An (3rd Edition) available 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.
Elementary Introduction to the Theory of Pseudodifferential Operators
Elementary Introduction to the Theory of Pseudodifferential Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elementary Introduction to the Theory of Pseudodifferential Operators write by Xavier Saint Raymond. This book was released on 2018-02-06. Elementary Introduction to the Theory of Pseudodifferential Operators available 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.
Pseudo-Differential Operators and Symmetries
Pseudo-Differential Operators and Symmetries - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Pseudo-Differential Operators and Symmetries write by Michael Ruzhansky. This book was released on 2009-12-29. Pseudo-Differential Operators and Symmetries available in PDF, EPUB and Kindle. 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.
Pseudodifferential and Singular Integral Operators
Pseudodifferential and Singular Integral Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Pseudodifferential and Singular Integral Operators write by Helmut Abels. This book was released on 2011-12-23. Pseudodifferential and Singular Integral Operators available 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.
Pseudo-differential Operators and the Nash-Moser Theorem
Pseudo-differential Operators and the Nash-Moser Theorem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Pseudo-differential Operators and the Nash-Moser Theorem write by Serge Alinhac. This book was released on 2007. Pseudo-differential Operators and the Nash-Moser Theorem available 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.
