Reconstructing Jacobi Matrices from Three Spectra

  • Johanna Michor
  • Gerald Teschl
Part of the Operator Theory: Advances and Applications book series (OT, volume 154)


Cut a Jacobi matrix into two pieces by removing the n-th column and n-th row. We give necessary and sufficient conditions for the spectra of the original matrix plus the spectra of the two submatrices to uniquely determine the original matrix. Our result contains Hochstadt’s theorem as a Special case.


Jacobi matrices spectral theory trace formulas Hochstadt’s theorem 


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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Johanna Michor
    • 1
    • 2
  • Gerald Teschl
    • 1
    • 2
  1. 1.Institut für MathematikWienAustria
  2. 2.International Erwin Schrödinger Institute for Mathematical PhysicsWienAustria

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