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The Resource Elliptic Theory and Noncommutative Geometry : Nonlocal Elliptic Operators, by Vladimir E. Nazaykinskiy, A. Yu. Savin, B. Yu. Sternin, (electronic resource)
Elliptic Theory and Noncommutative Geometry : Nonlocal Elliptic Operators, by Vladimir E. Nazaykinskiy, A. Yu. Savin, B. Yu. Sternin, (electronic resource)
Resource Information
The item Elliptic Theory and Noncommutative Geometry : Nonlocal Elliptic Operators, by Vladimir E. Nazaykinskiy, A. Yu. Savin, B. Yu. Sternin, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Elliptic Theory and Noncommutative Geometry : Nonlocal Elliptic Operators, by Vladimir E. Nazaykinskiy, A. Yu. Savin, B. Yu. Sternin, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 This comprehensive yet concise book deals with nonlocal elliptic differential operators, whose coefficients involve shifts generated by diffeomorophisms of the manifold on which the operators are defined. The main goal of the study is to relate analytical invariants (in particular, the index) of such elliptic operators to topological invariants of the manifold itself. This problem can be solved by modern methods of noncommutative geometry. This is the first and so far the only book featuring a consistent application of methods of noncommutative geometry to the index problem in the theory of nonlocal elliptic operators. Although the book provides important results, which are in a sense definitive, on the abovementioned topic, it contains all the necessary preliminary material, such as C*algebras and their Ktheory or cyclic homology. Thus the material is accessible for undergraduate students of mathematics (third year and beyond). It is also undoubtedly of interest for postgraduate students and scientists specializing in geometry, the theory of differential equations, functional analysis, etc. The book can serve as a good introduction to noncommutative geometry, which is one of the most powerful modern tools for studying a wide range of problems in mathematics and theoretical physics
 Language

 eng
 eng
 Edition
 1st ed. 2008.
 Extent
 1 online resource (232 p.)
 Note
 Description based upon print version of record
 Contents

 Analysis of Nonlocal Elliptic Operators
 Nonlocal Functions and Bundles
 Nonlocal Elliptic Operators
 Elliptic Operators over C*Algebras
 Homotopy Invariants of Nonlocal Elliptic Operators
 Homotopy Classification
 Analytic Invariants
 Bott Periodicity
 Direct Image and Index Formulas in KTheory
 Chern Character
 Cohomological Index Formula
 Cohomological Formula for the ?Index
 Index of Nonlocal Operators over C*Algebras
 Examples
 Index Formula on the Noncommutative Torus
 An Application of Higher Traces
 Index Formula for a Finite Group ?
 Isbn
 9781281491244
 Label
 Elliptic Theory and Noncommutative Geometry : Nonlocal Elliptic Operators
 Title
 Elliptic Theory and Noncommutative Geometry
 Title remainder
 Nonlocal Elliptic Operators
 Statement of responsibility
 by Vladimir E. Nazaykinskiy, A. Yu. Savin, B. Yu. Sternin
 Language

 eng
 eng
 Summary
 This comprehensive yet concise book deals with nonlocal elliptic differential operators, whose coefficients involve shifts generated by diffeomorophisms of the manifold on which the operators are defined. The main goal of the study is to relate analytical invariants (in particular, the index) of such elliptic operators to topological invariants of the manifold itself. This problem can be solved by modern methods of noncommutative geometry. This is the first and so far the only book featuring a consistent application of methods of noncommutative geometry to the index problem in the theory of nonlocal elliptic operators. Although the book provides important results, which are in a sense definitive, on the abovementioned topic, it contains all the necessary preliminary material, such as C*algebras and their Ktheory or cyclic homology. Thus the material is accessible for undergraduate students of mathematics (third year and beyond). It is also undoubtedly of interest for postgraduate students and scientists specializing in geometry, the theory of differential equations, functional analysis, etc. The book can serve as a good introduction to noncommutative geometry, which is one of the most powerful modern tools for studying a wide range of problems in mathematics and theoretical physics
 http://library.link/vocab/creatorName
 Nazaykinskiy, Vladimir E
 Dewey number
 515.7242
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut

 Q0GpKNUm1B0
 KpFAoZNsbo
 bAsXtJq43ss
 Language note
 English
 LC call number
 QA329329.9
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName

 Savin, A. Yu.
 Sternin, B. Yu.
 Series statement
 Advances in Partial Differential Equations,
 Series volume
 183
 http://library.link/vocab/subjectName

 Operator theory
 Operator Theory
 Label
 Elliptic Theory and Noncommutative Geometry : Nonlocal Elliptic Operators, by Vladimir E. Nazaykinskiy, A. Yu. Savin, B. Yu. Sternin, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents
 Analysis of Nonlocal Elliptic Operators  Nonlocal Functions and Bundles  Nonlocal Elliptic Operators  Elliptic Operators over C*Algebras  Homotopy Invariants of Nonlocal Elliptic Operators  Homotopy Classification  Analytic Invariants  Bott Periodicity  Direct Image and Index Formulas in KTheory  Chern Character  Cohomological Index Formula  Cohomological Formula for the ?Index  Index of Nonlocal Operators over C*Algebras  Examples  Index Formula on the Noncommutative Torus  An Application of Higher Traces  Index Formula for a Finite Group ?
 Dimensions
 unknown
 Edition
 1st ed. 2008.
 Extent
 1 online resource (232 p.)
 Form of item
 online
 Isbn
 9781281491244
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9783764387754
 Specific material designation
 remote
 System control number

 (CKB)1000000000440910
 (EBL)367337
 (OCoLC)272313415
 (SSID)ssj0000145541
 (PQKBManifestationID)11165442
 (PQKBTitleCode)TC0000145541
 (PQKBWorkID)10156930
 (PQKB)11611159
 (DEHe213)9783764387754
 (MiAaPQ)EBC367337
 (EXLCZ)991000000000440910
 Label
 Elliptic Theory and Noncommutative Geometry : Nonlocal Elliptic Operators, by Vladimir E. Nazaykinskiy, A. Yu. Savin, B. Yu. Sternin, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents
 Analysis of Nonlocal Elliptic Operators  Nonlocal Functions and Bundles  Nonlocal Elliptic Operators  Elliptic Operators over C*Algebras  Homotopy Invariants of Nonlocal Elliptic Operators  Homotopy Classification  Analytic Invariants  Bott Periodicity  Direct Image and Index Formulas in KTheory  Chern Character  Cohomological Index Formula  Cohomological Formula for the ?Index  Index of Nonlocal Operators over C*Algebras  Examples  Index Formula on the Noncommutative Torus  An Application of Higher Traces  Index Formula for a Finite Group ?
 Dimensions
 unknown
 Edition
 1st ed. 2008.
 Extent
 1 online resource (232 p.)
 Form of item
 online
 Isbn
 9781281491244
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9783764387754
 Specific material designation
 remote
 System control number

 (CKB)1000000000440910
 (EBL)367337
 (OCoLC)272313415
 (SSID)ssj0000145541
 (PQKBManifestationID)11165442
 (PQKBTitleCode)TC0000145541
 (PQKBWorkID)10156930
 (PQKB)11611159
 (DEHe213)9783764387754
 (MiAaPQ)EBC367337
 (EXLCZ)991000000000440910
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