Eleven pages of text (mainly formulae) and eleven pages of
appendices (proofs) are devoted to the rigorous formulation of the
biorthogonality and completeness of wave functions generated by
complex potentials admitting the presence of the so called spectral
singularities in the scattering dynamical regime.

The key result lies in the consistent incorporation of wave
functions related to spectral singularities into standard
biorthogonality and completeness formulae. The authors point out
that one of the most characteristic features of such a type of
result lies in the explicit relationship between the formulae and
the choice of the class of the test functions. Although the study
itself is restricted to a few sample Hamiltonians, similar projects
only started appearing in very recent literature [pars pro toto let
me mention paper ``Krein Spaces in de Sitter Quantum Theories" by
J.-P. Gazeau, P. Siegl and A. Youssef, SIGMA 6 (2010), item 011
(arXiv:1001.4810)].

MR2666950 Andrianov, A. A.; Cannata, F.; Sokolov, A. V. Spectral
singularities for non-Hermitian one-dimensional Hamiltonians:
puzzles with resolution of identity. J. Math. Phys. 51 (2010), no.
5, 052104, 22 pp. 81Q12 (34L10 34L40 47A10 47E05 47N50)