Solvable Algebras Of Pseudodifferential Operators

Author : Boris Plamenevskii,Oleg Sarafanov
Publisher : Springer Nature
Page : 249 pages
File Size : 41,6 Mb
Release : 2023-05-04
Category : Mathematics
ISBN : 9783031283987

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Solvable Algebras of Pseudodifferential Operators by Boris Plamenevskii,Oleg Sarafanov Pdf

This book presents original research results on pseudodifferential operators. C*-algebras generated by pseudodifferential operators with piecewise smooth symbols on a smooth manifold are considered. For each algebra, all the equivalence classes of irreducible representations are listed; as a consequence, a criterion for a pseudodifferential operator to be Fredholm is stated, the topology on the spectrum is described, and a solving series is constructed. Pseudodifferential operators on manifolds with edges are introduced, their properties are considered in details, and an algebra generated by the operators is studied. An introductory chapter includes all necessary preliminaries from the theory of pseudodifferential operators and C*-algebras.

Author : Boris Plamenevskii,Oleg Sarafanov
Publisher : Unknown
Page : 0 pages
File Size : 46,9 Mb
Release : 2023
Category : Electronic
ISBN : 3031283996

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Solvable Algebras of Pseudodifferential Operators by Boris Plamenevskii,Oleg Sarafanov Pdf

This book presents original research results on pseudodifferential operators. C*-algebras generated by pseudodifferential operators with piecewise smooth symbols on a smooth manifold are considered. For each algebra, all the equivalence classes of irreducible representations are listed; as a consequence, a criterion for a pseudodifferential operator to be Fredholm is stated, the topology on the spectrum is described, and a solving series is constructed. Pseudodifferential operators on manifolds with edges are introduced, their properties are considered in details, and an algebra generated by the operators is studied. An introductory chapter includes all necessary preliminaries from the theory of pseudodifferential operators and C*-algebras.

Author : Robert Lauter
Publisher : American Mathematical Soc.
Page : 114 pages
File Size : 49,7 Mb
Release : 2003
Category : Compact spaces
ISBN : 9780821832721

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Pseudodifferential Analysis on Conformally Compact Spaces by Robert Lauter Pdf

The $0$-calculus on a manifold with boundary is a micro-localization of the Lie algebra of vector fields that vanish at the boundary. It has been used by Mazzeo, Melrose to study the Laplacian of a conformally compact metric.

Author : P. A. Fillmore
Publisher : Springer
Page : 238 pages
File Size : 52,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540378082

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Proceedings of a Conference on Operator Theory by P. A. Fillmore Pdf

Author : Daniel Beltita,Mihai Sabac
Publisher : Birkhäuser
Page : 226 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883320

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Lie Algebras of Bounded Operators by Daniel Beltita,Mihai Sabac Pdf

In several proofs from the theory of finite-dimensional Lie algebras, an essential contribution comes from the Jordan canonical structure of linear maps acting on finite-dimensional vector spaces. On the other hand, there exist classical results concerning Lie algebras which advise us to use infinite-dimensional vector spaces as well. For example, the classical Lie Theorem asserts that all finite-dimensional irreducible representations of solvable Lie algebras are one-dimensional. Hence, from this point of view, the solvable Lie algebras cannot be distinguished from one another, that is, they cannot be classified. Even this example alone urges the infinite-dimensional vector spaces to appear on the stage. But the structure of linear maps on such a space is too little understood; for these linear maps one cannot speak about something like the Jordan canonical structure of matrices. Fortunately there exists a large class of linear maps on vector spaces of arbi trary dimension, having some common features with the matrices. We mean the bounded linear operators on a complex Banach space. Certain types of bounded operators (such as the Dunford spectral, Foia§ decomposable, scalar generalized or Colojoara spectral generalized operators) actually even enjoy a kind of Jordan decomposition theorem. One of the aims of the present book is to expound the most important results obtained until now by using bounded operators in the study of Lie algebras.

Author : H. Araki,R.V. Kadison
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461204534

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Mappings of Operator Algebras by H. Araki,R.V. Kadison Pdf

This volume consists of articles contributed by participants at the fourth Ja pan-U.S. Joint Seminar on Operator Algebras. The seminar took place at the University of Pennsylvania from May 23 through May 27, 1988 under the auspices of the Mathematics Department. It was sponsored and supported by the Japan Society for the Promotion of Science and the National Science Foundation (USA). This sponsorship and support is acknowledged with gratitude. The seminar was devoted to discussions and lectures on results and prob lems concerning mappings of operator algebras (C*-and von Neumann alge bras). Among the articles contained in these proceedings, there are papers dealing with actions of groups on C* algebras, completely bounded mappings, index and subfactor theory, and derivations of operator algebras. The seminar was held in honor of the sixtieth birthday of Sh6ichir6 Sakai, one of the great leaders of Functional Analysis for many decades. This vol ume is dedicated to Professor Sakai, on the occasion of that birthday, with the respect and admiration of all the contributors and the participants at the seminar. H. Araki Kyoto, Japan R. Kadison Philadelphia, Pennsylvania, USA Contents Preface.... ..... ....... ........... ...... ......... ................ ...... ............... ... vii On Convex Combinations of Unitary Operators in C*-Algebras UFFE HAAGERUP ......................................................................... .

Author : Michael Demuth
Publisher : De Gruyter Akademie Forschung
Page : 414 pages
File Size : 49,6 Mb
Release : 1996
Category : Mathematics
ISBN : UOM:39015041046973

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Schrödinger Operators, Markov Semigroups, Wavelet Analysis, Operator Algebras by Michael Demuth Pdf

The analysis of partial differential equations has stimulated large areas of research in mathematical physics, harmonic analysis, and operator theory. The present volume illuminates the depth and variety of these interactions. It begins with a survey on the use of semiclassical analysis and maximum-principle techniques in statistical mechanics. There follows an article presenting the perturbation theory for generators of Markov semigroups acting on Lp. The third contribution provides a self-contained introduction to continuous wavelet analysis, including its relations to function spaces and microlocal regularity; this is particularly topical, as wavelet methods have been applied with great success in the past decade to problems in harmonic and numerical analysis as well as in diverse fields of engineering. The final section explores pseudo-differential analysis on singular configurations, with special emphasis on C-algebra techniques, Mellin operators, and analytical index formulas.

Author : Xavier Saint Raymond
Publisher : CRC Press
Page : 118 pages
File Size : 41,6 Mb
Release : 1991-09-17
Category : Mathematics
ISBN : 0849371589

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Elementary Introduction to the Theory of Pseudodifferential Operators by Xavier Saint Raymond Pdf

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 : Daryl Geller
Publisher : Princeton University Press
Page : 504 pages
File Size : 53,7 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400860739

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Analytic Pseudodifferential Operators for the Heisenberg Group and Local Solvability. (MN-37) by Daryl Geller Pdf

Many of the operators one meets in several complex variables, such as the famous Lewy operator, are not locally solvable. Nevertheless, such an operator L can be thoroughly studied if one can find a suitable relative parametrix--an operator K such that LK is essentially the orthogonal projection onto the range of L. The analysis is by far most decisive if one is able to work in the real analytic, as opposed to the smooth, setting. With this motivation, the author develops an analytic calculus for the Heisenberg group. Features include: simple, explicit formulae for products and adjoints; simple representation-theoretic conditions, analogous to ellipticity, for finding parametrices in the calculus; invariance under analytic contact transformations; regularity with respect to non-isotropic Sobolev and Lipschitz spaces; and preservation of local analyticity. The calculus is suitable for doing analysis on real analytic strictly pseudoconvex CR manifolds. In this context, the main new application is a proof that the Szego projection preserves local analyticity, even in the three-dimensional setting. Relative analytic parametrices are also constructed for the adjoint of the tangential Cauchy-Riemann operator. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : B. A. Plamenevskii
Publisher : Unknown
Page : 291 pages
File Size : 46,6 Mb
Release : 1986
Category : Electronic
ISBN : OCLC:637749299

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Algebras of Pseudodifferential Operators by B. A. Plamenevskii Pdf

Author : François Trèves,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 46,8 Mb
Release : 1985
Category : Mathematics
ISBN : 9780821814697

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Pseudodifferential Operators and Applications by François Trèves,American Mathematical Society Pdf

"Proceedings of the Symposium on Pseudodifferential Operators and Fourier Integral Operators with Applications to Partial Differential Equations held at the University of Notre Dame, Notre Dame, Indiana, April 2-5, 1984"--T.p. verso.

Author : Heinz Otto Cordes
Publisher : Cambridge University Press
Page : 398 pages
File Size : 54,6 Mb
Release : 1995-02-23
Category : Mathematics
ISBN : 9780521378642

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The Technique of Pseudodifferential Operators by Heinz Otto Cordes Pdf

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.

Author : B. A. Plamenevskii
Publisher : Unknown
Page : 300 pages
File Size : 48,5 Mb
Release : 1989-10-31
Category : Electronic
ISBN : 9400923651

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Algebras of Pseudodifferential Operators by B. A. Plamenevskii Pdf

Author : M. Taylor
Publisher : Springer
Page : 160 pages
File Size : 49,6 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540372660

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Pseudo Differential Operators by M. Taylor Pdf

These notes are based on the lectures given on partial differential equations at the University of Michigan during the winter semester of 1972, with some extensions. The students to whom these lectures were addressed were assumed to have knowledge of elementary functional analysis, the Fourier transform, distribution theory, and Sobolev spaces, and such tools are used without comment. In this monography, we develop one tool, the calculus of pseudo differential operators, and apply it to several of the main problems of partial differential equations.

Author : Nicolas Lerner
Publisher : Springer Science & Business Media
Page : 397 pages
File Size : 55,9 Mb
Release : 2011-01-30
Category : Mathematics
ISBN : 9783764385101

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Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators by Nicolas Lerner Pdf

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.