Abstract: According to the relationship among the lattice vibrational Hamiltonian of one-two-and three-dimensional systems, the convolution law of phonon densities of states at different dimension is given. Discussions are made on the condition of convolution law, the physical figuration correlated to the densities of states and the possibility and limitation of this method. At last, some results of several systems are shown and remarked.

Key words: lattice vibration, dimensionality coherence, convolution law