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IMCS/Publications/BASM/Issues/BASM n2(108)-n3(109), 2025/

Dissipative Dirac Operator on Time Scales

Authors: Bilender P. Allahverdiev and Hüseyin Tuna
Keywords: Time scales, Dissipative Dirac operator, Self-adjoint dilation, Characteristic function, Completeness of the system of root vectors.

Abstract

In this paper, we study symmetric Dirac operator acting on time scales. We give maximal dissipative, maximal accumulative and self-adjoint extensions of such operator via the boundary conditions. Further, we construct a self-adjoint dilation of the maximal dissipative operator and 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 such operator are complete in the convenient Hilbert space .

Bilender P. Allahverdiev
Department of Mathematics,
Khazar University,
AZ1096 Baku, Azerbaijan
and
Research Center of Econophysics,
UNEC-Azerbaijan State University of Economics,
Baku, Azerbaijan
E-mail:

H¨useyin Tuna
Department of Mathematics,
Mehmet Akif Ersoy University,
15030 Burdur, Turkey
and
Research Center of Econophysics,
UNEC-Azerbaijan State University of Economics,
Baku, Azerbaijan
E-mail:

DOI

https://doi.org/10.56415/basm.y2025.i2-3.p3

Fulltext

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