Eigenvalues of a Continuous spectrum

Question

I'm stuck with this question: Given a self-adjoint linear operator A, consider the values ​​of u belonging to R(Real space) for which the resolver exists, is densely defined but is not limited. Discuss what the u values represent ​​in this case. if they exist,there are eigenfunctions of A associated to u? In what sense these latter can be seen as the limit of Hilbert space elements that are approximate eingenvector of A . Consider, for example, the case of the momentum operator.