Pseudo-Differential Operators, Singularities, Applications - 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, Singularities, Applications write by Iouri Egorov. This book was released on 2012-12-06. Pseudo-Differential Operators, Singularities, Applications available in PDF, EPUB and Kindle. 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.
Pseudo-Differential Operators on Manifolds with Singularities
Pseudo-Differential Operators on Manifolds with Singularities - 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 on Manifolds with Singularities write by B.-W. Schulze. This book was released on 1991-10-17. Pseudo-Differential Operators on Manifolds with Singularities available in PDF, EPUB and Kindle. 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.
Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators
Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential 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 Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators write by Nicolas Lerner. This book was released on 2011-01-30. Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators available in PDF, EPUB and Kindle. 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.
Pseudo-Differential Operators, Singularities, Applications
Pseudo-Differential Operators, Singularities, Applications - 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, Singularities, Applications write by Yu V Egorov. This book was released on 1997-03-20. Pseudo-Differential Operators, Singularities, Applications available in PDF, EPUB and Kindle.
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.
