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EDGE OPERATORS WITH CONDITIONS OF TOEPLITZ TYPE
Published online by Cambridge University Press: 05 September 2005
Abstract
Ellipticity of operators on a manifold with edges can be treated in the framework of a calculus of $2\times2$-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.
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- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 5 , Issue 1 , January 2006 , pp. 101 - 123
- Copyright
- 2005 Cambridge University Press
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