Dissipative operator and its Cayley transform

Uğurlu E., TAŞ K.

Turkish Journal of Mathematics, vol.41, no.6, pp.1404-1432, 2017 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 6
  • Publication Date: 2017
  • Doi Number: 10.3906/mat-1610-83
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1404-1432
  • Keywords: Cayley transform, Characteristic function, CMV matrix, Completely nonunitary contraction, Unitary colligation
  • Uşak University Affiliated: No

Abstract

In this paper, we investigate the spectral properties of the maximal dissipative extension of the minimal symmetric differential operator generated by a second order differential expression and dissipative and eigenparameter dependent boundary conditions. For this purpose we use the characteristic function of the maximal dissipative operator and inverse operator. This investigation is done by the characteristic function of the Cayley transform of the maximal dissipative operator, which is a completely nonunitary contraction belonging to the class C0: Using Solomyak's method we also introduce the self-adjoint dilation of the maximal dissipative operator and incoming/outgoing eigenfunctions of the dilation. Moreover, we investigate other properties of the Cayley transform of the maximal dissipative operator.