Abstract: The completeness of generalized eigenfunction system of the transport operator for a nonhomogeneous convex medium is discussed in this paper. By terms of the relative convergent method we recreat, we give a complete characterization for the problem of the completeness of generalized eigenfunction system of the transport operator. We show that if 0∈P_σ(E(t)), where {E(t) ≥ 0 is transport semigroup, then generalized eigenfunction system of transport operator is not complete. if O∉P_σ(E(t)), then the generalized eigenfunction system is complete only and only if it satisfies the condition of relative convergence.

Key words: transport operator, generalized eigenfunction system, completeness