Uniqueness theorems in inverse spectral theory for one-dimensional Schrödinger operators

Gesztesy, F.; Simon, B.

doi:10.1090/S0002-9947-96-01525-5

Uniqueness theorems in inverse spectral theory for one-dimensional Schrödinger operators
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by F. Gesztesy and B. Simon PDF

Trans. Amer. Math. Soc. 348 (1996), 349-373

Abstract:

New unique characterization results for the potential $V(x)$ in connection with Schrödinger operators on $\Bbb R$ and on the half-line $[0,\infty )$ are proven in terms of appropriate Krein spectral shift functions. Particular results obtained include a generalization of a well-known uniqueness theorem of Borg and Marchenko for Schrödinger operators on the half-line with purely discrete spectra to arbitrary spectral types and a new uniqueness result for Schrödinger operators with confining potentials on the entire real line.

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