Algebras Of Pseudodifferential Operators

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Solvable Algebras Of Pseudodifferential Operators

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Author : Boris Plamenevskii
language : en
Publisher: Springer Nature
Release Date : 2023-05-04

Solvable Algebras Of Pseudodifferential Operators written by Boris Plamenevskii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-04 with Mathematics categories.

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.

Algebras Of Pseudodifferential Operators

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Author : B.A. Plamenevskii
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Algebras Of Pseudodifferential Operators written by B.A. Plamenevskii 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 2012-12-06 with Mathematics categories.

One service mathematics has rendered the 'Et moi ..., si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point alle.' where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded non sense'. The series is divergent; therefore we may be Eric 1'. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Solvable Algebras Of Pseudodifferential Operators

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Author : Boris Plamenevskii
language : en
Publisher:
Release Date : 2023

Solvable Algebras Of Pseudodifferential Operators written by Boris Plamenevskii and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.

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.

Algebras Of Pseudodifferential Operators Near Edge And Corner Singularities

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Author : Christoph Dorschfeldt
language : en
Publisher: Wiley-VCH
Release Date : 1998-09-16

Algebras Of Pseudodifferential Operators Near Edge And Corner Singularities written by Christoph Dorschfeldt and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-16 with Mathematics categories.

This research monograph deals with analysis on manifolds with singularities. More precisely, it presents pseudodifferential operators near edges and corners. In particular, it considers parameter-dependent edge operators and edge operators of Mellin type. The investigation of such operator families is necessary to construct operator algebras on manifolds with higher singularities. A self-contained exposition in Mellin techniques and pseudodifferential operators with operator-valued symbols is given. The algebra of parameter-dependent edge operators is constructed. Finally, Mellin operators near corner singularities are investigated. The focus is on elliptic theory. Elliptic operators on manifolds with edges are constructed as well as parametrices to elliptic elements. The equivalence of ellipticity and the Fredholm property is shown. Close to corner singularities, edge operators of Mellin type are defined, a pseudodifferential calculus is presented and parametrices are constructed. Asymptotics are treated using analytic functions and the concept of continuous asymptotic types.

Algebras Of Pseudodifferential Operators

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Author : B. A. Plamenevskii
language : en
Publisher:
Release Date : 1989-10-31

Algebras Of Pseudodifferential Operators written by B. A. Plamenevskii and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-10-31 with categories.

Pseudodifferential Operators And Applications

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Author : Francois Treves
language : en
Publisher: American Mathematical Soc.
Release Date : 1985

Pseudodifferential Operators And Applications written by Francois Treves 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 1985 with Mathematics categories.

"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.

The Technique Of Pseudodifferential Operators

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Author : Heinz Otto Cordes
language : en
Publisher: Cambridge University Press
Release Date : 1995-02-23

The Technique Of Pseudodifferential Operators written by Heinz Otto Cordes and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-02-23 with Mathematics categories.

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.

Pseudo Differential Operators

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Author : Luigi Rodino
language : en
Publisher: American Mathematical Soc.
Release Date : 2007-11-21

Pseudo Differential Operators written by Luigi Rodino 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 2007-11-21 with Mathematics categories.

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.

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.

Operator Algebras Toeplitz Operators And Related Topics

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Author : Wolfram Bauer
language : en
Publisher: Birkhäuser
Release Date : 2021-09-02

Operator Algebras Toeplitz Operators And Related Topics written by Wolfram Bauer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-02 with Mathematics categories.

This book features a collection of up-to-date research papers that study various aspects of general operator algebra theory and concrete classes of operators, including a range of applications. Most of the papers included were presented at the International Workshop on Operator Algebras, Toeplitz Operators, and Related Topics, in Boca del Rio, Veracruz, Mexico, in November 2018. The conference, which was attended by more than 30 leading experts in the field, was held in celebration of Nikolai Vasilevski’s 70th birthday, and the contributions are dedicated to him.