Dissipative Dirac Operator with General Boundary Conditions on Time Scales

Allahverdiev B., Tuna H.

UKRAINIAN MATHEMATICAL JOURNAL, vol.72, no.5, pp.671-689, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 5
  • Publication Date: 2020
  • Doi Number: 10.1007/s11253-020-01808-8
  • Journal Name: UKRAINIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.671-689

Abstract

We consider symmetric Dirac operators on bounded time scales. Under general boundary conditions, we describe extensions (dissipative, accumulative, self-adjoint, etc.) of these symmetric operators. We construct a self-adjoint dilation of the dissipative operator. Hence, we determine the scattering matrix of dilation. Then 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.