Dissipative q-Dirac operator with general boundary conditions

Allahverdiev B., Tuna H.

QUAESTIONES MATHEMATICAE, vol.41, no.2, pp.239-255, 2018 (SCI-Expanded) identifier identifier

  • 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.