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We investigate the local density of states of the one-dimensional half-filledspinless fermion model with nearest-neighbor hopping t>0 and interaction V inits Luttinger liquid phase -2t < V <= 2t. The bulk density of states and thelocal density of states in open chains are calculated over the full band width4t with an energy resolution <= 0.08t using the dynamical density-matrixrenormalization group (DDMRG) method. We also perform DDMRG simulations with aresolution of 0.01t around the Fermi energy to reveal the power-law behaviourpredicted by the Luttinger liquid theory for bulk and boundary density ofstates. The exponents are determined using a finite-size scaling analysis ofDDMRG data for lattices with up to 3200 sites. The results agree with the exactexponents given by the Luttinger liquid theory combined with the Bethe Ansatzsolution. The crossover from boundary to bulk density of states is analyzed. Wehave found that boundary effects can be seen in the local density of states atall energies even far away from the chain edges.

Local density of states of the one-dimensional spinless fermion model