Journal d’Analyse Mathématique

, Volume 73, Issue 1, pp 267–297

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

Article

DOI: 10.1007/BF02788147

Cite this article as:
Gesztesy, F. & Simon, B. J. Anal. Math. (1997) 73: 267. doi:10.1007/BF02788147

Abstract

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 < ∞.

Copyright information

© 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