BANACH JOURNAL OF MATHEMATICAL ANALYSIS, cilt.7, sa.2, ss.194-207, 2013 (SCI İndekslerine Giren Dergi)
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)