Dissipative q-Dirac operator with general boundary conditions

  • Bilender P. Allahverdiev
  • Hüseyin Tuna
Keywords: Maximal dissipative operators, dissipative q-Dirac operator, self adjoint dilation, characteristic function, Blaschke-Potapov product, singular factor, completeness of the system of eigenfunctions

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.

Keywords: Maximal dissipative operators, dissipative q-Dirac operator, self adjoint dilation, characteristic function, Blaschke-Potapov product, singular factor, completeness of the system of eigenfunctions

Published
2018-03-03
Section
Articles

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606