95-268 Gesztesy F., Simon B.

Uniqueness Theorems in Inverse Spectral Theory for One-Dimensional Schr\"odinger Operators (76K, AMSTeX) Jun 14, 95

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Abstract. New unique characterization results for the potential $V(x)$ in connection with Schr\"odinger 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 Schr\"odinger operators on the half-line with purely discrete spectra to arbitrary spectral types and a new uniqueness result for Schr\"odinger operators with confining potentials on the entire real line.

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