Department of Mathematics, University of Missouri, Columbia, Missouri 65211 ; Division of Physics, Mathematics, and Astronomy, California Institute of Technology, 253-37, Pasadena, California 91125
Abstract:
New unique characterization results for the potential in connection with Schrödinger operators on and on the half-line 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.