Dissipative operator and its Cayley transform

Uğurlu E., TAŞ K.

Turkish Journal of Mathematics, cilt.41, sa.6, ss.1404-1432, 2017 (SCI-Expanded, Scopus, TRDizin) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 6
  • Basım Tarihi: 2017
  • Doi Numarası: 10.3906/mat-1610-83
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1404-1432
  • Anahtar Kelimeler: Cayley transform, Characteristic function, CMV matrix, Completely nonunitary contraction, Unitary colligation
  • Uşak Üniversitesi Adresli: Hayır

Özet

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.