Dissipative Dirac Operator on Time Scales

In this paper, we study symmetric Dirac operator acting on time scales. We give maximal dissipative, maximal accumulative and self-adjoint extensions of such operator via the boundary conditions. Further, we construct a self-adjoint dilation of the maximal dissipative operator and determine the scattering matrix of dilation. Later, we construct a functional model of this operator and define its characteristic function. Finally, we prove that all root vectors of such operator are complete in the convenient Hilbert space.