In this paper, we describe all maximal dissipative, maximal accretive and selfadjoint extensions of the minimal symmetric direct sum differential operators. Further using the equivalence of the Lax-Phillips scattering function and the Sz.-Nagy-Foias, characteristic function we show that all eigen and associated functions of the maximal dissipative extension of the minimal symmetric direct sum operator are complete in L-w(2) (Omega), where Omega = Omega(1) boolean OR Omega(2), Omega(1) = (0, c) and Omega(2) = c, infinity)