| 书目名称 | Elliptic Theory and Noncommutative Geometry | | 副标题 | Nonlocal Elliptic Op | | 编辑 | Vladimir E. Nazaikinskii,Anton Yu. Savin,Boris Yu. | | 视频video | | | 概述 | 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.Provides important results, wh | | 丛书名称 | Operator Theory: Advances and Applications | | 图书封面 |  | | 描述 | Noncommutative geometry, which can rightfully claim the role of a philosophy in mathematicalstudies,undertakesto replacegoodoldnotionsofclassicalgeometry (suchas manifolds,vectorbundles, metrics, di?erentiable structures,etc. ) by their abstract operator-algebraic analogs and then to study the latter by methods of the theory of operator algebras. At ?rst sight, this pursuit of maximum possible generality harbors the danger of completely forgetting the classical beginnings, so that not only the answers but also the questions would defy stating in traditional terms. Noncommutative geometry itself would become not only a method but also the main subject of investigation according to the capacious but not too practical formula: “Know thyself. ” Fortunately, this is not completely true (or even is completely untrue) in reality: there are numerous problems that are quite classical in their statement (or at least admit an equivalent classical statement) but can be solved only in the framework of noncommutative geometry. One of such problems is the subject of the present book. The classical elliptic theory developed in the well-known work of Atiyah and Singer on the index problem relates a | | 出版日期 | Book 2008 | | 关键词 | C* algebra; C*-algebra; Invariant; K-theory; cohomology; diffeomorphism; differential operator; elliptic op | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-7643-8775-4 | | isbn_ebook | 978-3-7643-8775-4Series ISSN 0255-0156 Series E-ISSN 2296-4878 | | issn_series | 0255-0156 | | copyright | Birkhäuser Basel 2008 |
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发表于 2025-3-21 16:55:26
