  We study a system of one-dimensional electrons in the regime of strong
repulsive interactions, where the spin exchange coupling J is small compared
with the Fermi energy, and the conventional Tomonaga-Luttinger theory does not
apply. We show that the tunneling density of states has a form of an asymmetric
peak centered near the Fermi level. In the spin-incoherent regime, where the
temperature is large compared to J, the density of states falls off as a power
law of energy \epsilon measured from the Fermi level, with the prefactor at
positive energies being twice as large as that at the negative ones. In
contrast, at temperatures below J the density of states forms a split peak with
most of the weight shifted to negative \epsilon.
