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

Gesztesy, F.

Simon, B.

English

. New unique characterization results for the potential V (x) in connection with Schrodinger operators on R and on the half-line [0; 1) 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 Schrodinger operators on the half-line with purely discrete spectra to arbitrary spectral types and a new uniqueness result for Schrodinger operators with confining potentials on the entire real line. x1. Introduction  The purpose of this article is to prove a variety of new uniqueness theorems for potentials V (x) in one-dimensional Schrodinger operators \Gamma  d  2  dx  2 + V on R and on the half-line R+ = [0; 1) in terms of appropriate Krein spectral shift functions recently introduced in a series of papers describing new trace formulas for V (x) on  R [15],[17],[19],[20] and on R+ [14]. First we briefly recall these trace formulas for Schrodinger operators H = \Gamma  d..

F. Gesztesy

B. Simon

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Uniqueness Theorems In Inverse Spectral Theory For One-Dimensional Schrödinger Operators

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

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

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