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