A New Method for Dissipative Dynamic Operator with Transmission Conditions

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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 \(C_{0}.\) 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.

Keywords

Time scale Dissipative operator Cayley transform Completely non-unitary contraction Unitary colligation Characteristic function CMV matrix 

Mathematics Subject Classification

Primary 34B20 Secondary 34N05 47B44 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Arts and SciencesÇankaya UniversityAnkaraTurkey

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