  The bulk-boundary correspondence in one dimension asserts that the physical
quantities defined in the bulk and at the edge are connected, as well
established in the argument for electric polarization. Recently, a spectral
bulk-boundary correspondence (SBBC), an extended version of the conventional
bulk-boundary correspondence to energy-dependent spectral functions, such as
Green's functions, has been proposed in chiral symmetric systems, in which the
chiral operator anticommutes with the Hamiltonian. In this study, we extend the
SBBC to a system with impurity scattering and dynamical self-energies,
regardless of the presence or absence of a gap in the energy spectrum.
Moreover, the SBBC is observed to hold even in a system without chiral
symmetry, which substantially generalizes its concept. The SBBC is demonstrated
with concrete models, such as superconducting nanowires and a normal metallic
chain. Its potential applications and certain remaining issues are also
discussed.
