锥点域的层势C* 代数-代数
Layer potentials C*-algebras of domains with conical points
摘要：
对于具有锥点Ω的区域，我们将一个自然C* 代数联系起来，这是由对Ω上边值问题的研究，特别是利用层势方法所激发的。在二维空间中，我们允许Ω是一个有分叉裂纹的区域。我们构造了一个与Ω的边界相关联的显式广群，并利用广群上的伪微分算子理论及其表示得到了我们的层势C* 代数.研究了它的结构，计算了相应的K-群，证明了隶属于该C* 代数的自然伪微分算子的Fredholm条件.
英文摘要：
To a domain with conical points Ω, we associate a natural C*-algebra that is motivated by the study of boundary value problems on Ω, especially using the method of layer potentials. In two dimensions, we allow Ωto be a domain with ramified cracks. We construct an explicit groupoid associated to the boundary of Ωand use the theory of pseudodifferential operators on groupoids and its representations to obtain our layer potentials C*-algebra. We study its structure, compute the associated K-groups, and prove Fredholm conditions for the natural pseudodifferential operators affiliated to this C*-algebra.
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