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• W2000984204 abstract "We consider a Dirac-type operator D P on a vector bundle V over a compact Riemannian manifold ( M , g ) with a non-empty boundary. The operator D P is specified by a boundary condition P ( u | ∂ M ) = 0 where P is a projector which may be a non-local, i.e., a pseudodifferential operator. We assume the existence of a chirality operator which decomposes L 2 ( M , V ) into two orthogonal subspaces X + ⊕ X − . Under certain conditions, the operator D P restricted to X + and X − defines a pair of Fredholm operators which maps X + → X − and X − → X + correspondingly, giving rise to a superstructure on V . In this paper we consider the questions of determining the index of D P and the reconstruction of ( M , g ) , V and D P from the boundary data on ∂ M . The data used is either the Cauchy data, i.e., the restrictions to ∂ M × R + of the solutions to the hyperbolic Dirac equation, or the boundary spectral data, i.e., the set of the eigenvalues and the boundary values of the eigenfunctions of D P . We obtain formulae for the index and prove uniqueness results for the inverse boundary value problems. We apply the obtained results to the classical Dirac-type operator in M × C 4 , M ⊂ R 3 ." @default.
• W2000984204 created "2016-06-24" @default.
• W2000984204 creator A5052627284 @default.
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• W2000984204 date "2009-05-01" @default.
• W2000984204 modified "2023-10-16" @default.
• W2000984204 title "Inverse problems and index formulae for Dirac operators" @default.
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• W2000984204 doi "https://doi.org/10.1016/j.aim.2008.12.001" @default.
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