- 95-268 Gesztesy F., Simon B.
- Uniqueness Theorems in Inverse Spectral Theory for
One-Dimensional Schr\"odinger Operators
Jun 14, 95
(auto. generated ps),
of related papers
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.