  By applying the Kramers-Kronig dispersion relation to the transmission
amplitude a direct connection of the conductance with the density of states is
given in quantum scattering systems connected to two one-channel leads.
  Using this method we show that in the Fano resonance the peak position of the
density of states is generally different from the position of the corresponding
conductance peak, whereas in the Breit-Wigner resonance those peak positions
coincide.
  The lineshapes of the density of states are well described by a Lorentz type
in the both resonances.
  These results are verified by another approach using a specific form of the
scattering matrix to describe scattering resonances.
