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- elliptic operators (6)
- manifolds with singularities (6)
- Fredholm property (5)
- boundary value problems (5)
- index (5)
- pseudodifferential operators (5)
- Boundary value problems (4)
- relative index (4)
- 'eta' invariant (3)
- Atiyah-Bott condition (3)
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- Institut für Mathematik (115) (remove)
We introduce a natural symmetry condition for a pseudodifferential operator on a manifold with cylindrical ends ensuring that the operator admits a doubling across the boundary. For such operators we prove an explicit index formula containing, apart from the Atiyah-Singer integral, a finite number of residues of the logarithmic derivative of the conormal symbol.
The paper is devoted to pseudodifferential boundary value problems in domains with singular points on the boundary. The tangent cone at a singular point is allowed to degenerate. In particular, the boundary may rotate and oscillate in a neighbourhood of such a point. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to singular points.