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)

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
Creator
Contributor
Author
Author
Subject
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 above-mentioned topic, it contains all the necessary preliminary material, such as C*-algebras and their K-theory or cyclic homology. Thus the material is accessible for undergraduate students of mathematics (third year and beyond). It is also undoubtedly of interest for post-graduate 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
Member of
Is Subseries of
http://library.link/vocab/creatorName
Nazaykinskiy, Vladimir E
Dewey number
515.7242
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • Q0GpKNUm1B0
  • KpFAoZN-sbo
  • bAsXtJq43ss
Language note
English
LC call number
QA329-329.9
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)
Instantiates
Publication
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 K-Theory -- 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
10.1007/978-3-7643-8775-4
Specific material designation
remote
System control number
  • (CKB)1000000000440910
  • (EBL)367337
  • (OCoLC)272313415
  • (SSID)ssj0000145541
  • (PQKBManifestationID)11165442
  • (PQKBTitleCode)TC0000145541
  • (PQKBWorkID)10156930
  • (PQKB)11611159
  • (DE-He213)978-3-7643-8775-4
  • (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)
Publication
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 K-Theory -- 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
10.1007/978-3-7643-8775-4
Specific material designation
remote
System control number
  • (CKB)1000000000440910
  • (EBL)367337
  • (OCoLC)272313415
  • (SSID)ssj0000145541
  • (PQKBManifestationID)11165442
  • (PQKBTitleCode)TC0000145541
  • (PQKBWorkID)10156930
  • (PQKB)11611159
  • (DE-He213)978-3-7643-8775-4
  • (MiAaPQ)EBC367337
  • (EXLCZ)991000000000440910

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