Eigenvalues and eigenfunctions associated with the Gel’fand–Levitan equation
- 1 January 1984
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 25 (1) , 108-112
- https://doi.org/10.1063/1.526004
Abstract
It is shown here that the solutions of the Gel’fand–Levitan equation for inverse potential scattering on the line may be expressed in terms of the eigenvalues and eigenfunctions of certain associated operators of trace class. The details are sketched for the case of rational reflection coefficients, and carried out for the simplest class of examples.Keywords
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