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Published January 1996 | Published
Journal Article Open

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

Abstract

New unique characterization results for the potential V(x) in connection with Schrödinger operators on R and on the half-line [0,∞)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.

Additional Information

© 1996 by the authors. Received by the editors February 27, 1995. This material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The U.S. Government has certain rights in this material.

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August 20, 2023
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