Spectral properties of the finite system of Klein-Gordon S-wave equations with condition depends on spectral parameter

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BAYRAM E., Arpat E. K.

Hacettepe Journal of Mathematics and Statistics, vol.54, no.4, pp.1300-1307, 2025 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 4
  • Publication Date: 2025
  • Doi Number: 10.15672/hujms.1393132
  • Journal Name: Hacettepe Journal of Mathematics and Statistics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.1300-1307
  • Keywords: eigenvalues, Klein-Gordon S-wave equation, spectral singularities
  • Gazi University Affiliated: Yes

Abstract

The spectral characteristics of the operator L are studied where L is defined within the Hilbert space L2(ℝ+, ℂV ) given by a finite system of Klein-Gordon type differential equations and boundary condition depends on spectral parameter. The research of the KleinGordon type operator continues to be an important topic for researchers due to the range of applicability of them in numerous branches of mathematics and quantum physics. Contrary to the previous works, we take the potential as complex valued and generalize the problem to the matrix Klein-Gordon operator case. The spectrum is derived by determining the Jost function and resolvent operator of the prescribed operator. Further, we provide the conditions that must be met for the certain quantitative properties of the spectrum.