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Author : Samuel Zaidman
Publisher : Harlow, England : Longman Scientific & Technical
Page : 136 pages
File Size : 53,6 Mb
Release : 1991
Category : Differential operators
ISBN : UCSD:31822006762819
Author : Xavier Saint Raymond
Publisher : Routledge
Page : 71 pages
File Size : 46,7 Mb
Release : 2018-02-06
Category : Mathematics
ISBN : 9781351452922
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 : Man Wah Wong
Publisher : World Scientific
Page : 156 pages
File Size : 44,8 Mb
Release : 1999
Category : Mathematics
ISBN : 9810238134
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
Author : M W Wong
Publisher : World Scientific Publishing Company
Page : 196 pages
File Size : 41,6 Mb
Release : 2014-03-11
Category : Mathematics
ISBN : 9789814583107
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 : Samuel Zaidman
Publisher : Unknown
Page : 124 pages
File Size : 45,5 Mb
Release : 1991
Category : Electronic
ISBN : 0608036242
Author : Gerd Grubb
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 48,5 Mb
Release : 2008-10-14
Category : Mathematics
ISBN : 9780387848945
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.
Author : Stevan Pilipović,Joachim Toft
Publisher : Birkhäuser
Page : 290 pages
File Size : 50,6 Mb
Release : 2015-04-27
Category : Mathematics
ISBN : 9783319146188
This book gathers peer-reviewed contributions representing modern trends in the theory of generalized functions and pseudo-differential operators. It is dedicated to Professor Michael Oberguggenberger (Innsbruck University, Austria) in honour of his 60th birthday. The topics covered were suggested by the ISAAC Group in Generalized Functions (GF) and the ISAAC Group in Pseudo-Differential Operators (IGPDO), which met at the 9th ISAAC congress in Krakow, Poland in August 2013. Topics include Columbeau algebras, ultra-distributions, partial differential equations, micro-local analysis, harmonic analysis, global analysis, geometry, quantization, mathematical physics, and time-frequency analysis. Featuring both essays and research articles, the book will be of great interest to graduate students and researchers working in analysis, PDE and mathematical physics, while also offering a valuable complement to the volumes on this topic previously published in the OT series.
Author : Serge Alinhac,Patrick Gérard
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 45,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821834541
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 : Shahla Molahajloo,Stevan Pilipović,Joachim Toft,M. W. Wong
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 51,6 Mb
Release : 2013-02-26
Category : Mathematics
ISBN : 9783034805858
This volume consists of twenty peer-reviewed papers from the special session on pseudodifferential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples’ Friendship University of Russia in Moscow on August 22‒27, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifolds with edges, heat kernels and Green functions of sub-Laplacians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, Lp-boundedness of pseudo-differential operators on the torus, and pseudo-differential operators related to time-frequency analysis. The second group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlinear differential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differential equations. This second group of papers are related to the third collection of papers via the setting of Colombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volume contains the synergies of the three areas treated and is a useful complement to volumes 155, 164, 172, 189, 205 and 213 published in the same series in, respectively, 2004, 2006, 2007, 2009, 2010 and 2011.
Author : Michael Ruzhansky,Ville Turunen
Publisher : Springer Science & Business Media
Page : 712 pages
File Size : 55,8 Mb
Release : 2009-12-29
Category : Mathematics
ISBN : 9783764385149
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 : Heinz O. Cordes
Publisher : Springer
Page : 339 pages
File Size : 40,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540384632
Author : André Unterberger
Publisher : Birkhäuser
Page : 202 pages
File Size : 53,6 Mb
Release : 2015-06-22
Category : Mathematics
ISBN : 9783319186573
The main results of this book combine pseudo differential analysis with modular form theory. The methods rely for the most part on explicit spectral theory and the extended use of special functions. The starting point is a notion of modular distribution in the plane, which will be new to most readers and relates under the Radon transformation to the classical one of modular form of the non-holomorphic type. Modular forms of the holomorphic type are addressed too in a more concise way, within a general scheme dealing with quantization theory and elementary, but novel, representation-theoretic concepts.
Author : Bent E. Petersen
Publisher : Pitman Advanced Publishing Program
Page : 376 pages
File Size : 45,7 Mb
Release : 1983
Category : Mathematics
ISBN : UOM:39015015693370
Author : Luigi Rodino,M. W. Wong,Hongmei Zhu
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 48,5 Mb
Release : 2011-03-14
Category : Mathematics
ISBN : 9783034800495
This volume consists of eighteen peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at Imperial College London on July 13-18, 2009. Featured in this volume are the analysis, applications and computations of pseudo-differential operators in mathematics, physics and signal analysis. This volume is a useful complement to the volumes “Advances in Pseudo-Differential Operators”, “Pseudo-Differential Operators and Related Topics”, “Modern Trends in Pseudo-Differential Operators”, “New Developments in Pseudo-Differential Operators” and “Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations” published in the same series in, respectively, 2004, 2006, 2007, 2009 and 2010.
Author : Bert-Wolfgang Schulze,M. W. Wong
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 44,9 Mb
Release : 2010-03-01
Category : Mathematics
ISBN : 9783034601986
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.