Edge operators with conditions of Toeplitz type
- Ellipticity of operators on a manifold with edges can be treated in the framework of a calculus of 2 X 2-block matrix operators with trace and potential operators on the edges. The picture is similar to the pseudodifferential analysis of boundary-value problems. The extra conditions satisfy an analogue of the Shapiro-Lopatinskij condition, provided a topological obstruction for the elliptic edge-degenerate operator in the upper left corner vanishes; this is an analogue of a condition of Atiyah and Bott in boundary-value problems. In general, however, we need global projection data, similarly to global boundary conditions, known for Dirac operators or other geometric operators. The present paper develops a new calculus with global projection data for operators on manifolds with edges. In particular, we show the Fredholm property in a suitable scale of spaces and construct parametrices within the calculus
Author details: | Bert-Wolfgang SchulzeGND, Jörg Seiler |
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Publication type: | Article |
Language: | English |
Year of first publication: | 2006 |
Publication year: | 2006 |
Release date: | 2017/03/24 |
Source: | Journal of the institute of mathematics of jussieu. - 5 (2006), 1, S. 101 - 123 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |