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Advances in Partial Differential Equations

Elliptic Theory and Noncommutative Geometry

Nonlocal Elliptic Operators

Authors: Nazaykinskiy, Vladimir E., Savin, A. Yu., Sternin, B. Yu.

  • First book featuring a consistent application of methods of noncommutative geometry to the index problem in the theory of nonlocal elliptic operators
  • Provides important results and at the same time contains all the necessary preliminary material, thus being effectively self-contained
  • Comprehensive and yet concise - attractive for readers at any level
  • Can serve as a concise introduction to noncommutative geometry
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Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-7643-8775-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-3-7643-8774-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Table of contents (15 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-7643-8775-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-3-7643-8774-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Elliptic Theory and Noncommutative Geometry
Book Subtitle
Nonlocal Elliptic Operators
Authors
Series Title
Advances in Partial Differential Equations
Series Volume
183
Copyright
2008
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-8775-4
DOI
10.1007/978-3-7643-8775-4
Hardcover ISBN
978-3-7643-8774-7
Series ISSN
2504-3587
Edition Number
1
Number of Pages
XII, 224
Topics