Reflectionless potentials and point interactions in Pontryagin spaces
The problem of constructing generalized point interactions of the second derivative operator in L-2( R) leading to the same scattering data as for reflectionless potentials is considered. It is proved that this problem has a solution only if extensions in Pontryagin spaces are involved. The solution of the inverse scattering problem is not unique, this is illustrated by considering the scattering