Open AccessDissipative Dirac operator with general boundary conditions on time scales
Author(s) -
Bilender P. Allahverdiev,
Hüseyin Tuna
Publication year - 2020
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v72i5.546
Subject(s) - dissipative system , dilation (metric space) , dirac operator , mathematics , operator (biology) , dissipative operator , boundary value problem , bounded function , mathematical analysis , boundary (topology) , pure mathematics , mathematical physics , physics , quantum mechanics , combinatorics , biochemistry , chemistry , repressor , transcription factor , gene
UDC 517.9In 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.