C Algebras And Elliptic Theory Ii

Author : Anonim
Publisher : Unknown
Page : 309 pages
File Size : 48,6 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 0817686037

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C*-algebras and Elliptic Theory II by Anonim Pdf

Author : Bogdan Bojarski,Alexander S. Mishchenko,Evgenij V. Troitsky,Andrzej Weber
Publisher : Springer Science & Business Media
Page : 327 pages
File Size : 54,5 Mb
Release : 2006-11-09
Category : Mathematics
ISBN : 9783764376871

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C*-algebras and Elliptic Theory by Bogdan Bojarski,Alexander S. Mishchenko,Evgenij V. Troitsky,Andrzej Weber Pdf

This book consists of reviewed original research papers and expository articles in index theory (especially on singular manifolds), topology of manifolds, operator and equivariant K-theory, Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others, and applications in mathematical physics. The wide spectrum of subjects reflects the diverse directions of research for which the starting point was the Atiyah-Singer index theorem.

Author : Dan Burghelea,Richard Melrose,Alexander S. Mishchenko,Evgenij V. Troitsky
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 43,6 Mb
Release : 2008-03-18
Category : Mathematics
ISBN : 9783764386047

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C*-algebras and Elliptic Theory II by Dan Burghelea,Richard Melrose,Alexander S. Mishchenko,Evgenij V. Troitsky Pdf

This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.

Author : Vladimir E. Nazaykinskiy,A. Yu. Savin,B. Yu. Sternin
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 41,5 Mb
Release : 2008-06-30
Category : Mathematics
ISBN : 9783764387754

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Elliptic Theory and Noncommutative Geometry by Vladimir E. Nazaykinskiy,A. Yu. Savin,B. Yu. Sternin Pdf

This comprehensive yet concise book deals with nonlocal elliptic differential operators. These are operators whose coefficients involve shifts generated by diffeomorphisms of the manifold on which the operators are defined. This is the first book featuring a consistent application of methods of noncommutative geometry to the index problem in the theory of nonlocal elliptic operators. To make the book self-contained, the authors have included necessary geometric material.

Author : I_U_ri_ Petrovich Solov_‘v Evgeni_ Vadimovich Troit_s_ki_
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 41,6 Mb
Release : 2000-10-03
Category : Mathematics
ISBN : 0821897934

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C * -Algebras and Elliptic Operators in Differential Topology by I_U_ri_ Petrovich Solov_‘v Evgeni_ Vadimovich Troit_s_ki_ Pdf

The aim of this book is to present some applications of functional analysis and the theory of differential operators to the investigation of topological invariants of manifolds. The main topological application discussed in the book concerns the problem of the description of homotopy-invariant rational Pontryagin numbers of non-simply connected manifolds and the Novikov conjecture of homotopy invariance of higher signatures. The definition of higher signatures and the formulation of the Novikov conjecture are given in Chapter 3. In this chapter, the authors also give an overview of different approaches to the proof of the Novikov conjecture. First, there is the Mishchenko symmetric signature and the generalized Hirzebruch formulae and the Mishchenko theorem of homotopy invariance of higher signatures for manifolds whose fundamental groups have a classifying space, being a complete Riemannian non-positive curvature manifold. Then the authors present Solovyov's proof of the Novikov conjecture for manifolds with fundamental group isomorphic to a discrete subgroup of a linear algebraic group over a local field, based on the notion of the Bruhat-Tits building. Finally, the authors discuss the approach due to Kasparov based on the operator $KK$-theory and another proof of the Mishchenko theorem. In Chapter 4, they outline the approach to the Novikov conjecture due to Connes and Moscovici involving cyclic homology. That allows one to prove the conjecture in the case when the fundamental group is a (Gromov) hyperbolic group. The text provides a concise exposition of some topics from functional analysis (for instance, $C^*$-Hilbert modules, $K$-theory or $C^*$-bundles, Hermitian $K$-theory, Fredholm representations, $KK$-theory, and functional integration) from the theory of differential operators (pseudodifferential calculus and Sobolev chains over $C^*$-algebras), and from differential topology (characteristic classes). The book explains basic ideas of the subject and can serve as a course text for an introduction to the study of original works and special monographs.

Author : Jerome Kaminker,Kenneth C. Millett,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 53,6 Mb
Release : 1988
Category : Mathematics
ISBN : 9780821850770

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Index Theory of Elliptic Operators, Foliations, and Operator Algebras by Jerome Kaminker,Kenneth C. Millett,American Mathematical Society Pdf

Combining analysis, geometry, and topology, this volume provides an introduction to current ideas involving the application of $K$-theory of operator algebras to index theory and geometry. In particular, the articles follow two main themes: the use of operator algebras to reflect properties of geometric objects and the application of index theory in settings where the relevant elliptic operators are invertible modulo a $C^*$-algebra other than that of the compact operators. The papers in this collection are the proceedings of the special sessions held at two AMS meetings: the Annual meeting in New Orleans in January 1986, and the Central Section meeting in April 1986. Jonathan Rosenberg's exposition supplies the best available introduction to Kasparov's $KK$-theory and its applications to representation theory and geometry. A striking application of these ideas is found in Thierry Fack's paper, which provides a complete and detailed proof of the Novikov Conjecture for fundamental groups of manifolds of non-positive curvature. Some of the papers involve Connes' foliation algebra and its $K$-theory, while others examine $C^*$-algebras associated to groups and group actions on spaces.

Author : Nora Doll,Hermann Schulz-Baldes,Nils Waterstraat
Publisher : Walter de Gruyter GmbH & Co KG
Page : 460 pages
File Size : 41,7 Mb
Release : 2023-06-19
Category : Mathematics
ISBN : 9783111172477

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Spectral Flow by Nora Doll,Hermann Schulz-Baldes,Nils Waterstraat Pdf

Author : Daniel Alpay,Victor Vinnikov
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 49,6 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783764373030

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Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations by Daniel Alpay,Victor Vinnikov Pdf

This volume contains a selection of papers, from experts in the area, on multidimensional operator theory. Topics considered include the non-commutative case, function theory in the polydisk, hyponormal operators, hyperanalytic functions, and holomorphic deformations of linear differential equations. Operator Theory, Systems Theory and Scattering Theory will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.

Author : Vladimir Nazaikinskii,Bert-Wolfgang Schulze,Boris Sternin
Publisher : Springer Science & Business Media
Page : 122 pages
File Size : 41,8 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9783034805100

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The Localization Problem in Index Theory of Elliptic Operators by Vladimir Nazaikinskii,Bert-Wolfgang Schulze,Boris Sternin Pdf

The book deals with the localization approach to the index problem for elliptic operators. Localization ideas have been widely used for solving various specific index problems for a long time, but the fact that there is actually a fundamental localization principle underlying all these solutions has mostly passed unnoticed. The ignorance of this general principle has often necessitated using various artificial tricks and hindered the solution of new important problems in index theory. So far, the localization principle has been only scarcely covered in journal papers and not covered at all in monographs. The suggested book is intended to fill the gap. So far, it is the first and only monograph dealing with the topic. Both the general localization principle and its applications to specific problems, existing and new, are covered. The book will be of interest to working mathematicians as well as graduate and postgraduate university students specializing in differential equations and related topics.​

Author : Pavel Exner
Publisher : American Mathematical Soc.
Page : 721 pages
File Size : 48,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821844717

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Analysis on Graphs and Its Applications by Pavel Exner Pdf

This book addresses a new interdisciplinary area emerging on the border between various areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus here is on problems and techniques related to graphs, quantum graphs, and fractals that parallel those from differential equations, differential geometry, or geometric analysis. Also included are such diverse topics as number theory, geometric group theory, waveguide theory, quantum chaos, quantum wiresystems, carbon nano-structures, metal-insulator transition, computer vision, and communication networks.This volume contains a unique collection of expert reviews on the main directions in analysis on graphs (e.g., on discrete geometric analysis, zeta-functions on graphs, recently emerging connections between the geometric group theory and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide systems and modeling quantum graph systems with waveguides, control theory on graphs), as well as research articles.

Author : Steven Lord,Fedor Sukochev,Dmitriy Zanin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 304 pages
File Size : 43,8 Mb
Release : 2021-07-19
Category : Mathematics
ISBN : 9783110392319

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Theory by Steven Lord,Fedor Sukochev,Dmitriy Zanin Pdf

This book is the second edition of the first complete study and monograph dedicated to singular traces. The text offers, due to the contributions of Albrecht Pietsch and Nigel Kalton, a complete theory of traces and their spectral properties on ideals of compact operators on a separable Hilbert space. The second edition has been updated on the fundamental approach provided by Albrecht Pietsch. For mathematical physicists and other users of Connes’ noncommutative geometry the text offers a complete reference to traces on weak trace class operators, including Dixmier traces and associated formulas involving residues of spectral zeta functions and asymptotics of partition functions.

Author : Herbert Schröder
Publisher : Chapman and Hall/CRC
Page : 184 pages
File Size : 54,7 Mb
Release : 1993-08-23
Category : Mathematics
ISBN : UOM:39015029969386

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K-Theory for Real C*-Algebras and Applications by Herbert Schröder Pdf

This Research Note presents the K-theory and KK-theory for real C*-algebras and shows that these can be successfully applied to solve some topological problems which are not accessible to the tools developed in the complex setting alone.

Author : Bernhelm Booss,Krzysztof P. Wojciechowski
Publisher : World Scientific
Page : 553 pages
File Size : 53,5 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812773609

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Analysis, Geometry and Topology of Elliptic Operators by Bernhelm Booss,Krzysztof P. Wojciechowski Pdf

Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics. The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski''s work in the theory of elliptic operators. Sample Chapter(s). Contents (42 KB). Contents: On the Mathematical Work of Krzysztof P Wojciechowski: Selected Aspects of the Mathematical Work of Krzysztof P Wojciechowski (M Lesch); Gluing Formulae of Spectral Invariants and Cauchy Data Spaces (J Park); Topological Theories: The Behavior of the Analytic Index under Nontrivial Embedding (D Bleecker); Critical Points of Polynomials in Three Complex Variables (L I Nicolaescu); Chern-Weil Forms Associated with Superconnections (S Paycha & S Scott); Heat Kernel Calculations and Surgery: Non-Laplace Type Operators on Manifolds with Boundary (I G Avramidi); Eta Invariants for Manifold with Boundary (X Dai); Heat Kernels of the Sub-Laplacian and the Laplacian on Nilpotent Lie Groups (K Furutani); Remarks on Nonlocal Trace Expansion Coefficients (G Grubb); An Anomaly Formula for L 2- Analytic Torsions on Manifolds with Boundary (X Ma & W Zhang); Conformal Anomalies via Canonical Traces (S Paycha & S Rosenberg); Noncommutative Geometry: An Analytic Approach to Spectral Flow in von Neumann Algebras (M-T Benameur et al.); Elliptic Operators on Infinite Graphs (J Dodziuk); A New Kind of Index Theorem (R G Douglas); A Note on Noncommutative Holomorphic and Harmonic Functions on the Unit Disk (S Klimek); Star Products and Central Extensions (J Mickelsson); An Elementary Proof of the Homotopy Equivalence between the Restricted General Linear Group and the Space of Fredholm Operators (T Wurzbacher); Theoretical Particle, String and Membrane Physics, and Hamiltonian Dynamics: T-Duality for Non-Free Circle Actions (U Bunke & T Schick); A New Spectral Cancellation in Quantum Gravity (G Esposito et al.); A Generalized Morse Index Theorem (C Zhu). Readership: Researchers in modern global analysis and particle physics.

Author : W. Arveson
Publisher : Springer Science & Business Media
Page : 117 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461263715

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An Invitation to C*-Algebras by W. Arveson Pdf

This book gives an introduction to C*-algebras and their representations on Hilbert spaces. We have tried to present only what we believe are the most basic ideas, as simply and concretely as we could. So whenever it is convenient (and it usually is), Hilbert spaces become separable and C*-algebras become GCR. This practice probably creates an impression that nothing of value is known about other C*-algebras. Of course that is not true. But insofar as representations are con cerned, we can point to the empirical fact that to this day no one has given a concrete parametric description of even the irreducible representations of any C*-algebra which is not GCR. Indeed, there is metamathematical evidence which strongly suggests that no one ever will (see the discussion at the end of Section 3. 4). Occasionally, when the idea behind the proof of a general theorem is exposed very clearly in a special case, we prove only the special case and relegate generalizations to the exercises. In effect, we have systematically eschewed the Bourbaki tradition. We have also tried to take into account the interests of a variety of readers. For example, the multiplicity theory for normal operators is contained in Sections 2. 1 and 2. 2. (it would be desirable but not necessary to include Section 1. 1 as well), whereas someone interested in Borel structures could read Chapter 3 separately. Chapter I could be used as a bare-bones introduction to C*-algebras. Sections 2.

Author : Vladimir Georgiev,Tohru Ozawa,Michael Ruzhansky,Jens Wirth
Publisher : Springer Nature
Page : 317 pages
File Size : 45,5 Mb
Release : 2020-11-07
Category : Mathematics
ISBN : 9783030582159

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Advances in Harmonic Analysis and Partial Differential Equations by Vladimir Georgiev,Tohru Ozawa,Michael Ruzhansky,Jens Wirth Pdf

This book originates from the session "Harmonic Analysis and Partial Differential Equations" held at the 12th ISAAC Congress in Aveiro, and provides a quick overview over recent advances in partial differential equations with a particular focus on the interplay between tools from harmonic analysis, functional inequalities and variational characterisations of solutions to particular non-linear PDEs. It can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.