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Communications in Mathematical Physics

, Volume 115, Issue 4, pp 595–605 | Cite as

Ann-dimensional Borg-Levinson theorem

  • Adrian Nachman
  • John Sylvester
  • Gunther Uhlmann
Article

Abstract

We show that the potentialq is uniquely determined by the spectrum, and boundary values of the normal derivatives of the eigenfunctions of the Schrödinger operator −Δ+q with Dirichlet boundary conditions on a bounded domain Ω in ℝ n . This and related results can be viewed as a direct generalization of the theorem in the title, which states that the spectrum and the norming constants determine the potential in the one dimensional case.

Keywords

Boundary Condition Neural Network Statistical Physic Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Adrian Nachman
    • 1
  • John Sylvester
    • 2
    • 3
  • Gunther Uhlmann
    • 4
  1. 1.Mathematics DepartmentUniversity of RochesterRochesterUSA
  2. 2.Courant Institute of Math. Science, Mathematics DepartmentYale UniversityDurhamUSA
  3. 3.Courant Institute of Math. Science, Mathematics DepartmentMathematics Department Duke UniversityDurhamUSA
  4. 4.Department of MathematicsUniversity of WashingtonSeattleUSA

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