Journal d’Analyse Mathématique

, Volume 73, Issue 1, pp 267–297

m-Functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices



We study inverse spectral analysis for finite and semi-infinite Jacobi matricesH. Our results include a new proof of the central result of the inverse theory (that the spectral measure determinesH). We prove an extension of the theorem of Hochstadt (who proved the result in casen = N) thatn eigenvalues of anN × N Jacobi matrixH can replace the firstn matrix elements in determiningH uniquely. We completely solve the inverse problem for (δn, (H-z)-1 δn) in the caseN < ∞.


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© Hebrew University of Jerusalem 1997

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Division of Physics, Mathematics, and AstronomyCalifornia Institute of TechnologyPasadenaUSA

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