On the spectrum of singular Hahn-Sturm-Liouville operators


Allahverdiev B. P. , TUNA H.

ADVANCED STUDIES-EURO-TBILISI MATHEMATICAL JOURNAL, vol.15, no.3, pp.75-90, 2022 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.32513/asetmj/19322008225
  • Journal Name: ADVANCED STUDIES-EURO-TBILISI MATHEMATICAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.75-90
  • Keywords: Hahn-Sturm-Liouville operator, splitting method, discrete spectrum, continuous spectrum, EQUATIONS, CRITERIA
  • Süleyman Demirel University Affiliated: Yes

Abstract

In this paper, we study the spectrum of Hahn-Sturm-Liouville operators. In this context, it is shown that the regular symmetric Hahn-Sturm-Liouville operator is semi-bounded from below. Moreover, we give some conditions for the self-adjoint singular Hahn-Sturm-Liouville operator to have a discrete spectrum. The method of proof is based on the splittings technique. Finally, we investigate the continuous spectrum of this operator.