  Resolutions of identity for certain non-Hermitian Hamiltonians constructed
from biorthogonal sets of their eigen- and associated functions are given for
the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under
consideration possess the continuous spectrum and the following peculiarities
are investigated: (1) the case when there is an exceptional point of arbitrary
multiplicity situated on a boundary of continuous spectrum; (2) the case when
there is an exceptional point situated inside of continuous spectrum. The
reductions of the derived resolutions of identity under narrowing of the
classes of employed test functions are revealed. It is shown that in the case
(1) some of associated functions included into the resolution of identity are
normalizable and some of them may be not and in the case (2) the bounded
associated function corresponding to the exceptional point does not belong to
the physical state space. Spectral properties of a SUSY partner Hamiltonian for
the Hamiltonian with an exceptional point are examined.
