Uniqueness and numerical recovery of a potential on the real line

Abstract

We consider the recovery of the potential q(x) in the singular problem Under suitable conditions the coefficient is uniquely determined from the set of flux data at the origin corresponding to the source terms , which constitute a basis for . To facilitate numerical recovery, the problem is formulated as an infinite-dimensional least-squares minimization problem. Tikhonov regularization is employed, and the resulting problem is discretized via sinc collocation. Several numerical examples are included.