Spectral problems of dissipative singular q-Sturm-Liouville operators in limit-circle case

We consider the dissipative singular q-Sturm-Liouville operators acting in Hilbert space L2 w,q(R+), that extensions of a minimal symmetric operator with deficiency indices (2, 2) (in limit-circle case).We construct self-adjoint dilation and its incoming outgoing spectral representations, which make it possible to determine scattering matrix terms Weyl-Titchmarsh function operator. also functional model characteristic (or function). Theorems on completeness system or root functions accumulative are proved.