Non-self-adjoint singular matrix Sturm–Liouville operators with general boundary conditions

Allahverdiev B.

Filomat, vol.38, no.30, pp.10505-10518, 2024 (SCI-Expanded) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 38 Say: 30
  • Nəşr tarixi: 2024
  • Doi nömrəsi: 10.2298/fil2430505a
  • jurnalın adı: Filomat
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.10505-10518
  • Açar sözlər: characteristic function, completeness of the system of root vectors, functional model, maximal dissipative operator, scattering matrix, self-adjoint dilation, Singular matrix Sturm–Liouville operator
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

In the Hilbert space L2 (I; E) (I:= [a, b), −∞ < a < b ≤ +∞, dim E = m < +∞, A > 0), the A maximal dissipative singular matrix-valued Sturm–Liouville operators that the extensions of a minimal symmetric operator with maximal deficiency indices (2m, 2m) (in limit-circle case at singular endpoint b) are studied. The maximal dissipative operators with general (for example coupled or separated) boundary conditions are investigated. A self-adjoint dilation is constructed for dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We also construct a functional model of the dissipative operator and determine its characteristic function in terms of the scattering matrix of the dilation (or in terms of the Weyl function of self-adjoint operator). Moreover a theorem on completeness of the system of eigenvectors and associated vectors (or root vectors) of the dissipative operators proved.