Dissipative Dirac operator with general boundary conditions on time scales

B. P. Allahverdiev; H.  Tuna

doi:10.37863/umzh.v72i5.546

B. P. Allahverdiev Department of Mathematics, Süleyman Demirel University, Isparta, Turkey
H. Tuna Mehmet Akif Ersoy Univ., Burdur, Turkey https://orcid.org/0000-0001-7240-8687

DOI: https://doi.org/10.37863/umzh.v72i5.546

Abstract

UDC 517.9

In this paper, we consider the symmetric Dirac operator on bounded time scales. With general boundary conditions, we describe extensions (dissipative, accumulative, self-adjoint and the other) of such symmetric operators. 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.

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