Elliptic Theory and Noncommutative Geometry: Nonlocal Elliptic Operators (Operator Theory: Advances and Applications / Advances in Partial Differential Equations) [Hardcover]

Vladimir E. Nazaykinskiy (Author), A. Yu. Savin (Author), B. Yu. Sternin (Author)

Book Description

ISBN-10: 3764387742 | ISBN-13: 978-3764387747 | Publication Date: June 23, 2008 | Edition: 1

The 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. The main goal of the study is to relate analytical invariants (in particular, the index) of such operators to topological invariants of the manifold itself. This problem can be solved by modern methods of noncommutative geometry. To make the book self-contained, the authors have included necessary geometric material (C*-algebras and their K-theory, cyclic homology, etc.).

Editorial Reviews

From the Back Cover

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.

Product Details

• Hardcover: 224 pages
• Publisher: Birkhäuser Basel; 1 edition (June 23, 2008)
• Language: English
• ISBN-10: 3764387742
• ISBN-13: 978-3764387747
• Product Dimensions: 9.2 x 6.5 x 0.7 inches
• Shipping Weight: 1.3 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #572,165 in Books (See Top 100 in Books)