Analysis Of Pseudo Differential Operators
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Pseudo Differential Operators And Symmetries
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Author : Michael Ruzhansky
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-29
Pseudo Differential Operators And Symmetries written by Michael Ruzhansky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-29 with Mathematics categories.
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.
Introduction To Pseudo Differential Operators An 3rd Edition
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Author : Man-wah Wong
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-03-11
Introduction To Pseudo Differential Operators An 3rd Edition written by Man-wah Wong and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-11 with Mathematics categories.
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.
Pseudo Differential Operators Complex Analysis And Partial Differential Equations
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Author : Bert-Wolfgang Schulze
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-01
Pseudo Differential Operators Complex Analysis And Partial Differential Equations written by Bert-Wolfgang Schulze and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-01 with Mathematics categories.
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.
Elementary Introduction To The Theory Of Pseudodifferential Operators
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Author : Xavier Saint Raymond
language : en
Publisher: Routledge
Release Date : 2018-02-06
Elementary Introduction To The Theory Of Pseudodifferential Operators written by Xavier Saint Raymond and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-06 with Mathematics categories.
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
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Author : Louis Nirenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-06
Pseudo Differential Operators written by Louis Nirenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-06 with Mathematics categories.
S. Agmon: Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators.- J. Bokobza-Haggiag: Une définition globale des opérateurs pseudo-différentiels sur une variété différentiable.- L. Boutet de Monvel: Pseudo-differential operators and analytic function.- A. Calderon: A priori estimates for singular integral operators.- B.F. Jones: Characterization of spaces of Bessel potentials related to the heat equation.- J.J. Kohn: Pseudo-differential operators and non-elliptic problems.- R.T. Seeley: Topics in pseudo-differential operators.- I.M. E. Shamir: Boundary value problems for elliptic convolution systems.- Singer: Elliptic operators on manifolds.
Metrics On The Phase Space And Non Selfadjoint Pseudo Differential Operators
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Author : Nicolas Lerner
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-30
Metrics On The Phase Space And Non Selfadjoint Pseudo Differential Operators written by Nicolas Lerner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-30 with Mathematics categories.
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.
The Analysis Of Linear Partial Differential Operators Iii
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Author : Lars Hörmander
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-15
The Analysis Of Linear Partial Differential Operators Iii written by Lars Hörmander and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-15 with Mathematics categories.
From the reviews: "Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators." L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987. "This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation." J. Brüning in Zentralblatt MATH, 1987.
Pseudo Differential Operators And The Nash Moser Theorem
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Author : Serge Alinhac
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Pseudo Differential Operators And The Nash Moser Theorem written by Serge Alinhac and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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.
Analysis Of Pseudo Differential Operators
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Author : Shahla Molahajloo
language : en
Publisher: Springer
Release Date : 2019-05-08
Analysis Of Pseudo Differential Operators written by Shahla Molahajloo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-08 with Mathematics categories.
This volume, like its predecessors, is based on the special session on pseudo-differential operators, one of the many special sessions at the 11th ISAAC Congress, held at Linnaeus University in Sweden on August 14-18, 2017. It includes research papers presented at the session and invited papers by experts in fields that involve pseudo-differential operators. The first four chapters focus on the functional analysis of pseudo-differential operators on a spectrum of settings from Z to Rn to compact groups. Chapters 5 and 6 discuss operators on Lie groups and manifolds with edge, while the following two chapters cover topics related to probabilities. The final chapters then address topics in differential equations.
Pseudodifferential Methods In Number Theory
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Author : André Unterberger
language : en
Publisher: Birkhäuser
Release Date : 2018-07-16
Pseudodifferential Methods In Number Theory written by André Unterberger and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-16 with Mathematics categories.
Classically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic. The operators which make up the main subject of the book can be characterized in terms of congruence arithmetic. They enjoy a Eulerian structure, and are applied to the search for new conditions equivalent to the Riemann hypothesis. These consist in the validity of certain parameter-dependent estimates for a class of Hermitian forms of finite rank. The Littlewood criterion, involving sums of Möbius coefficients, and the Weil so-called explicit formula, which leads to his positivity criterion, fit within this scheme, using in the first case Weyl's pseudodifferential calculus, in the second case Fuchs'. The book should be of interest to people looking for new possible approaches to the Riemann hypothesis, also to new perspectives on pseudodifferential analysis and on the way it combines with modular form theory. Analysts will have no difficulty with the arithmetic aspects, with which, save for very few exceptions, no previous acquaintance is necessary.