Tunneling into a periodically modulated Luttinger liquid

We study the tunneling into the edge of the Luttinger liquid with periodically modulated concentration of electrons. It is shown that the modulation,by causing a gap in the spectrum of plasmons, leads to an additional anomaly in the density of states at frequency corresponding to the center of the gap. The shape of the anomaly depends strongly on the {\em phase} of the modulation. The sensitivity to the phase is related to the plasmon mode, localized at the edge, its frequency lying within the gap (analog of the Tamm state for an electron in an interrupted periodic potential).