Pseudo Differential Operators On Manifolds With Singularities
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| Author | : B.-W. Schulze |
| Publisher | : Elsevier |
| Total Pages | : 417 |
| Release | : 1991-10-17 |
| Genre | : Mathematics |
| ISBN | : 0080875459 |
The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics.The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.
| Author | : Iouri Egorov |
| Publisher | : Birkhäuser |
| Total Pages | : 360 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034889003 |
This book grew out of lecture notes based on the DMV seminar "Pseudo- Differential Operators, Singularities, Applications" held by the authors in Reisenburg-Günzburg, 12–19 July 1992. The modern theory of elliptic boundary value problems in domains having conical or edge singularities on the boundary as well as the classical theory of elliptic boundary value problems and the original Kondratiev theory are presented. This material forms the foundation for the second part of the book which contains a new construction of pseudo-differential operators with symbols corresponding to the singularities of the boundary of different dimensions. This allows in particular to obtain complete asymptotic expansions of solutions near these singularities.
| Author | : Luigi Rodino |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 432 |
| Release | : 2007-11-21 |
| Genre | : Mathematics |
| ISBN | : 9780821871553 |
This volume is based on lectures given at the workshop on pseudo-differential operators held at the Fields Institute from December 11, 2006 to December 15, 2006. The two main themes of the workshop and hence this volume are partial differential equations and time-frequency analysis. The contents of this volume consist of five mini-courses for graduate students and post-docs, and fifteen papers on related topics. Of particular interest in this volume are the mathematical underpinnings, applications and ramifications of the relatively new Stockwell transform, which is a hybrid of the Gabor transform and the wavelet transform. The twenty papers in this volume reflect modern trends in the development of pseudo-differential operators.
| Author | : Bert-Wolfgang Schulze |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 294 |
| Release | : 2010-03-01 |
| Genre | : Mathematics |
| ISBN | : 3034601980 |
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.
| Author | : Michael E. Taylor |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 274 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821843788 |
Developing three related tools that are useful in the analysis of partial differential equations (PDEs) arising from the classical study of singular integral operators, this text considers pseudodifferential operators, paradifferential operators, and layer potentials.
| Author | : Man-wah Wong |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 195 |
| Release | : 2014-03-11 |
| Genre | : Mathematics |
| ISBN | : 9814583103 |
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 | : Luigi Rodino |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 337 |
| Release | : 2009-01-06 |
| Genre | : Mathematics |
| ISBN | : 3764389699 |
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.
| Author | : Juan Gil |
| Publisher | : Birkhäuser |
| Total Pages | : 574 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034878508 |
Boundary problems constitute an essential field of common mathematical interest, they lie in the center of research activities both in analysis and geometry. This book encompasses material from both disciplines, and focuses on their interactions which are particularly apparent in this field. Moreover, the survey style of the contributions makes the topics accessible to a broad audience with a background in analysis or geometry, and enables the reader to get a quick overview.
| Author | : M. W. Wong |
| Publisher | : Birkhäuser |
| Total Pages | : 242 |
| Release | : 2017-01-20 |
| Genre | : Mathematics |
| ISBN | : 3319475126 |
This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.
| Author | : Heinz Otto Cordes |
| Publisher | : Cambridge University Press |
| Total Pages | : 398 |
| Release | : 1995-02-23 |
| Genre | : Mathematics |
| ISBN | : 0521378648 |
Pseudodifferential operators arise naturally in a solution of boundary problems for partial differential equations. The formalism of these operators serves to make the Fourier-Laplace method applicable for nonconstant coefficient equations. This book presents the technique of pseudodifferential operators and its applications, especially to the Dirac theory of quantum mechanics. The treatment uses 'Leibniz formulas' with integral remainders or as asymptotic series. While a pseudodifferential operator is commonly defined by an integral formula, it also may be described by invariance under action of a Lie group. The author discusses connections to the theory of C*-algebras, invariant algebras of pseudodifferential operators under hyperbolic evolution, and the relation of the hyperbolic theory to the propagation of maximal ideals. The Technique of Pseudodifferential Operators will be of particular interest to researchers in partial differential equations and mathematical physics.
