Spectral decomposition of a perturbed differential operator (Q752305)

It is known that a non-selfadjoint perturbation of the continuous spectrum causes spectral singularities. As a rule, eigenfunction expansions are considered for cases where the spectral singularities are embedded into the continuous spectrum. In the author's papers [Ukr. Mat. Zh. 33, 227-233 (1981; Zbl 0464.47026, ibid. 35, 467-472 (1983; Zbl 0533.47026)] the case was considered where the spectral singularities are located at the ends of the interval of the continuous spectrum. In this paper it is shown by examples that the scheme developed there applies also to the case where the continuous spectrum occupies a half-axis.