Fields of Dirichlet spaces: continuity, approximation, and stability

狄利克雷空间的域：连续性、近似性和稳定性

• 批准号: 515076870
• 负责人: Professor Dr. Batu Güneysu
• 金额: --
• 依托单位: Université de Sousse
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/515076870?language=en
• 关键词: Fields; Dirichlet; spaces; continuity; approximation

The project focuses on the development of new concepts for continuous fields of Dirichlet spaces over varying spaces and the application to different types of example classes. Dirichlet spaces are suitable because of their numerous applications as well as because of their methodological diversity: Dirichlet forms or Dirichlet spaces combine analytic, geometric and probabilistic structures in a natural way. The aspects of continuity, approximation and stability for fields of Dirichlet spaces therefore also concern geometric and spectral theoretical data, which are given by the Dirichlet forms and whose control is particularly important in many application areas. In two major subprojects the abstract concepts are applied to more specific situations. On the one hand, by considering singular example classes, such as Dirichlet-to-Neumann operators and more general traces of Dirichlet forms. On the other hand, to fields of Riemannian manifolds and more general metric measure spaces, where the fields are sometimes defined by flows.

该项目的重点是发展新概念的连续领域的狄利克雷空间在不同的空间和应用程序的不同类型的例子类。狄利克雷空间是合适的，因为它们的许多应用，以及因为它们的方法多样性：狄利克雷形式或狄利克雷空间联合收割机结合分析，几何和概率结构在一个自然的方式。因此，狄利克雷空间领域的连续性、近似性和稳定性也涉及到几何和谱理论数据，这些数据由狄利克雷形式给出，并且其控制在许多应用领域中特别重要。在两个主要的子项目中，抽象的概念被应用于更具体的情况。一方面，通过考虑奇异的例子类，如Dirichlet-to-Neumann算子和更一般的Dirichlet形式的迹。另一方面，黎曼流形和更一般的度量测度空间的域，其中域有时由流定义。