Numerical technique for the inverse resonance problem

摘要

Motivated by the work of Regge (Nuovo Cimento 8 (1958) 671; 9 (1958) 491) we are interested in the problem of recovering a radial potential in R3 from its resonance parameters, which are zeros of the appropriately defined Jost function. For a potential of compact support these may in turn be identified as the complex eigenvalues of a nonselfadjoint Sturm–Liouville problem with an eigenparameter dependent boundary condition. In this paper we propose and study a particular computational technique for this problem, based on a moment problem for a function g(t) which is related to the boundary values of the corresponding Gelfand–Levitan kernel.