510 Mathematik
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- relative index (5)
- Fredholm property (3)
- conormal symbol (3)
- elliptic operators (3)
- index theory (3)
- surgery (3)
- Atiyah-Bott obstruction (2)
- Lefschetz fixed point formula (2)
- conical singularities (2)
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- elliptic families (2)
- elliptic family (2)
- elliptic operator (2)
- index formulas (2)
- manifold with singularities (2)
- manifolds with conical singularities (2)
- quantization (2)
- regularizer (2)
- symmetry conditions (2)
- (co)boundary operator (1)
- APS problem (1)
- Fredholm operators (1)
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- Riemann-Roch theorem (1)
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- contact transformations (1)
- edge symbol (1)
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- elliptic problem (1)
- ellipticity (1)
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- index (1)
- index formula (1)
- manifold with edge (1)
- manifolds with edges (1)
- nonhomogeneous boundary value problems (1)
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- pseudo-diferential operators (1)
- pseudodiferential operators (1)
- regularizers (1)
- spectral flow (1)
- spectral resolution (1)
- symplectic (canonical) transformations (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.
For elliptic operators on manifolds with boundary, we define spectral boundary value problems, which generalize the Atiyah-Patodi-Singer problem to the case of nonhomogeneous boundary conditions, operators of arbitrary order, and nonself-adjoint conormal symbols. The Fredholm property is proved and equivalence with certain elliptic equations on manifolds with conical singularities is established.