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Article Dans Une Revue Journal of Spectral Theory Année : 2018

A multidimensional Borg-Levinson theorem for magnetic Schrödinger operators with partial spectral data

Résumé

We consider the multidimensional Borg-Levinson theorem of determining both the magnetic field dA and the electric potential V , appearing in the Dirichlet realization of the magnetic Schrödinger operator H = (−i∇ + A) 2 + V on a bounded domain Ω ⊂ R n , n ≥ 2, from partial knowledge of the boundary spectral data of H. The full boundary spectral data are given by the set {(λ k , ∂ν ϕ k |∂Ω) : k ≥ 1}, where {λ k : k ∈ N * } is the non-decreasing sequence of eigenvalues of H, {ϕ k : k ∈ N * } an associated Hilbertian basis of eigenfunctions and ν is the unit outward normal vector to ∂Ω. We prove that some asymptotic knowledge of (λ k , ∂ν ϕ k |∂Ω) with respect to k ≥ 1 determines uniquely the magnetic field dA and the electric potential V .
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Dates et versions

hal-01143482 , version 1 (17-04-2015)
hal-01143482 , version 2 (29-04-2015)
hal-01143482 , version 3 (30-04-2015)
hal-01143482 , version 4 (13-10-2016)

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Yavar Kian. A multidimensional Borg-Levinson theorem for magnetic Schrödinger operators with partial spectral data. Journal of Spectral Theory, 2018, 8 (1), pp.235-269. ⟨10.4171/JST/195⟩. ⟨hal-01143482v4⟩
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