, Volume 73, Issue 1, pp 267-297

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

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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 (δ n , (H-z)-1 δ n ) in the caseN < ∞.

This material is based upon work supported by the National Science Foundation under Grant Nos. DMS-9623121 and DMS-9401491.