m-Functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices
- Cite this article as:
- Gesztesy, F. & Simon, B. J. Anal. Math. (1997) 73: 267. doi:10.1007/BF02788147
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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 < ∞.