  We describe the Fano asymmetry by expanding the transmission amplitude with
respect to states with point spectra (discrete eigenstates), including not only
bound states but also resonant states with complex eigenvalues. We first
introduce a novel complete set that spans the Hilbert space of the central part
of an open quantum-dot system. This complete set contains all states of point
spectra, but does not contain any states of continuous spectra. We thereby
analytically expand the conductance of the dot in terms of all discrete states
without any background integrals. This expansion implies that the resonant
states produce the main contributions to the electron transmission. We then
explain the Fano peak as an interference effect involving resonant states. We
find that there are three types of Fano asymmetry according to their origins:
the interference between a resonant state and an anti-resonant state, that
between a resonant state and a bound state, and that between two resonant
states. We derive microscopic expressions of the Fano parameters that describe
the three types of Fano asymmetry. We show that the last two types display the
asymmetric energy dependence given by Fano, but the first one shows a slightly
different form.
