Dissipative q-Dirac operator with general boundary conditions
QUAESTIONES MATHEMATICAE, vol.41, no.2, pp.239-255, 2018 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 41 Issue: 2
- Publication Date: 2018
- Doi Number: 10.2989/16073606.2017.1377309
- Journal Name: QUAESTIONES MATHEMATICAE
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.239-255
- Keywords: Maximal dissipative operators, dissipative q-Dirac operator, self adjoint dilation, characteristic function, Blaschke-Potapov product, singular factor, completeness of the system of eigenfunctions, DILATION
- Süleyman Demirel University Affiliated: Yes
Abstract
In this paper, we consider the symmetric q-Dirac operator. We describe dissipative, accumulative, self-adjoint and the other extensions of such operators with general boundary conditions. We construct a self-adjoint dilation of dissipative operator. Hence, we 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 this operator are complete.