Some spectral problems of dissipative q-Sturm–Liouville operators in limit-point case for q > 1

Allahverdiev B., AYGAR KÜÇÜKEVCİLİOĞLU Y.

Filomat, vol.38, no.22, pp.7693-7705, 2024 (SCI-Expanded) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 38 Say: 22
  • Nəşr tarixi: 2024
  • Doi nömrəsi: 10.2298/fil2422693a
  • jurnalın adı: Filomat
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.7693-7705
  • Açar sözlər: Characteristic func-tion, Completeness of the root functions, Dissipative operator, q-Sturm–Liouville equation, Self-adjoint dilation, Weyl–Titchmarsh function
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

The main purpose of this study is to investigate dissipative singular q-Sturm–Liouville operators in a suitable Hilbert space and to examine the extensions of a minimal symmetric operator in limit-point case. We make a self-adjoint dilation of the dissipative operator together with its incoming and outgoing spectral components, which satisfy determining the scattering function of the dilation via Lax-Phillips theory. We also construct a functional model of the maximal dissipative operator by using the incoming spectral representation and we find its characteristic function in terms of the Weyl–Titchmarsh function of the self-adjoint q-Sturm–Liouville operator whenever q > 1. Furthermore, we present a theorem about the completeness of the system of eigenfunctions and associated functions (or root functions) of the dissipative q-Sturm–Liouville operator.