Layer potentials C*-algebras of domains with conical points

Details Layer potentials C*-algebras of domains with conical points Layer potentials C*-algebras of domains with conical points

2011-11-24

arxiv.org/abs/1111.5754v1

Mathematics

Operator Algebras

30 pages

Scientific paper

To a domain with conical points \Omega, we associate a natural C*-algebra that is motivated by the study of boundary value problems on \Omega, especially using the method of layer potentials. In two dimensions, we allow \Omega to be a domain with ramified cracks. We construct an explicit groupoid associated to the boundary of \Omega and 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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