A New Method for Dissipative Dynamic Operator with Transmission Conditions

Uğurlu E., TAŞ K.

Complex Analysis and Operator Theory, vol.12, no.4, pp.1027-1055, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.1007/s11785-017-0732-y
  • Journal Name: Complex Analysis and Operator Theory
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1027-1055
  • Keywords: Cayley transform, Characteristic function, CMV matrix, Completely non-unitary contraction, Dissipative operator, Time scale, Unitary colligation
  • Uşak University Affiliated: No

Abstract

In this paper, we investigate the spectral properties of a boundary value transmission problem generated by a dynamic equation on the union of two time scales. For such an analysis we assign a suitable dynamic operator which is in limit-circle case at infinity. We also show that this operator is a simple maximal dissipative operator. Constructing the inverse operator we obtain some information about the spectrum of the dissipative operator. Moreover, using the Cayley transform of the dissipative operator we pass to the contractive operator which is of the class C0. With the aid of the minimal function we obtain more information on the dissipative operator. Finally, we investigate other properties of the contraction such that multiplicity of the contraction, unitary colligation with basic operator and CMV matrix representation associated with the contraction.