Nonstrictly hyperbolic systems of conservation laws of the conjugate type |
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Authors: | Hermano Frid Marcelo M Santos |
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Institution: | 1. Instituto de Matemá tica,Universidade Federal do Rio de Janeiro , RJ, C.Postal 68530, CEP 21 945, Brazil;2. Departamento de Matemática , Universidade Federal da Paraíba , Jo?o Pessoa, PB, CEP 58 059-900, Brazil |
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Abstract: | We consider an inverse boundary problem for a general second order self-adjoint elliptic differential operator on a compact differential manifold with boundary. The inverse problem is that of the reconstruction of the manifold and operator via all but finite number of eigenvalues and traces on the boundary of the corresponding eigenfunctions of the operator. We prove that the data determine the manifold and the operator to within the group of the generalized gauge transformations. The proof is based upon a procedure of the reconstruction of a canonical object in the orbit of the group. This object, the canonical Schrödinger operator, is uniquely determined via its incomplete boundary spectral data. |
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