On quantum star graphs with eigenparameter dependent vertex conditions

Mutlu G., Uğurlu E.

ANALYSIS AND MATHEMATICAL PHYSICS, cilt.13, sa.4, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 4
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s13324-023-00822-w
  • Dergi Adı: ANALYSIS AND MATHEMATICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Gazi Üniversitesi Adresli: Evet

Özet

We investigate the spectral properties of two different boundary value problems on a compact star graph in which the vertex conditions are dependent on the spectral parameter. We treat these boundary value problems as eigenvalue problems in some extended Hilbert spaces by associating them with vector-valued operators. We prove that the corresponding operators are self-adjoint. We construct the characteristic functions of these eigenvalue problems and prove that the corresponding operators have discrete spectrum. Moreover, we present some examples where we construct fundamental solutions and derive the resolvent operators.