Layer potentials C*-algebras of domains with conical points

• Autorzy: Catarina Carvalho , Yu Qiao
• Języki publikacji: EN

Abstrakty

EN

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 Ω to be a domain with ramified cracks. We construct an explicit groupoid associated to ∂Ω 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.

Słowa kluczowe

EN

Layer potentials method; Conical domains; Desingularization; Groupoid C*-algebras; Weighted Sobolev spaces; Fredholmness

Kategorie tematyczne

• 47G30: Pseudodifferential operators
• 31B10: Integral representations, integral operators, integral equations methods
• 47L80: Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
• 22A22: Topological groupoids (including differentiable and Lie groupoids)
• 58H05: Pseudogroups and differentiable groupoids
• 31A10: Integral representations, integral operators, integral equations methods
• 46L80: K -theory and operator algebras (including cyclic theory)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 1
• Strony: 27-54

Daty

wydano

2013-01-01

online

2012-10-24

Twórcy

autor

Catarina Carvalho

• UTL

autor

Yu Qiao

• Nankai University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0066-y