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- 1998 (37) (remove)
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Keywords
- manifolds with singularities (3)
- 'eta' invariant (2)
- Fredholm property (2)
- differential operators (2)
- elliptic complexes (2)
- index (2)
- pseudodifferential operators (2)
- Atiyah-Patodi-Singer theory (1)
- Chern character (1)
- Fredholm operators (1)
- Hodge theory (1)
- Lefschetz fixed point formula (1)
- Lefschetz number (1)
- boundary value problems (1)
- cohomology (1)
- conical singularities (1)
- contact transformations (1)
- elliptic operator (1)
- ellipticity (1)
- index formulas (1)
- index of elliptic operator (1)
- integral formulas (1)
- manifolds with conical singularities (1)
- manifolds with edges (1)
- meromorphic family (1)
- monodromy matrix (1)
- pseudodiferential operators (1)
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- quantization (1)
- regularizer (1)
- regularizers (1)
- relative cohomology (1)
- residue (1)
- spectral boundary value problems (1)
- ∂-operator (1)
Institute
The quantization of contact transformations of the cosphere bundle over a manifold with conical singularities is described. The index of Fredholm operators given by this quantization is calculated. The answer is given in terms of the Epstein-Melrose contact degree and the conormal symbol of the corresponding operator.
In the paper we study the possibility to represent the index formula for spectral boundary value problems as a sum of two terms, the first one being homotopy invariant of the principal symbol, while the second depends on the conormal symbol of the problem only. The answer is given in analytical, as well as in topological terms.
The paper is devoted to pseudodifferential boundary value problems in domains with cuspidal wedges. Concerning the geometry we even admit a more general behaviour, namely oscillating cuspidal wedges. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to edges.