Deformation Theory for Boundary Value Problems

边值问题的变形理论

• 批准号: 5413496
• 负责人: Professor Dr. Elmar Schrohe
• 金额: --
• 依托单位: Institut für Analysis
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2004
• 资助国家: 德国
• 起止时间: 2003-12-31 至 2008-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5413496?language=en
• 关键词: Deformation; Theory; Boundary; Value; Problems

It is the aim of this project to construct a deformation quantization associated to the algebra of all operators of order and class (type) zero in Boutet de Monvel's calculus for R-n+ and, more generally, for a compact manifold with boundary. Part of the project is to determine the continuous field of C*-algebras associated to this deformation, thus extending Connes' notion of the tangent groupoid to the case of manifolds with boundary. Eventually we hope to be able to combine this with the techniques of Nest and Tsygan to derive a new approach to index theory for boundary value problems. In a parallel study we want to consider the corresponding problems for the Heisenberg calculus on foliated manifolds. This project is of major interest in itself. It continues the investigation of Boutet de Monvel's calculus from an operator-algebraic point of view. At the same time it may be seen as a test for the approach to index theory developed by Nest and Tsygan.

这个项目的目的是构造一个变形量子化，它与Boutet de Monvel的R-n+演算中的所有阶和类（类型）为零的算子的代数相关，更一般地说，是一个有边界的紧致流形。该项目的一部分是确定与这种变形相关的C*-代数的连续域，从而将Connes的切群胚概念扩展到有边界流形的情况。最后，我们希望能够将联合收割机与Nest和Tsygan的技术结合起来，导出一种新的边值问题指数理论方法。在一个平行的研究中，我们要考虑相应的问题，为海森堡演算的叶流形。这个项目本身就很重要。它继续调查布泰德蒙维尔的演算从算子代数的观点。与此同时，它可以被视为对Nest和Tsygan开发的指数理论方法的测试。