Quantum Graph Realization of Transmission Problems

MUTLU G.

3rd International Conference on Mathematics and its Applications in Science and Engineering, ICMASE 2022, Bucharest, Romanya, 4 - 07 Temmuz 2022, cilt.414, ss.23-31 identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 414
  • Doi Numarası: 10.1007/978-3-031-21700-5_3
  • Basıldığı Şehir: Bucharest
  • Basıldığı Ülke: Romanya
  • Sayfa Sayıları: ss.23-31
  • Anahtar Kelimeler: Boundary value problems, Quantum graphs, Self-adjoint operators, Transmission problems
  • Gazi Üniversitesi Adresli: Evet

Özet

In this study, the relations between boundary value transmission problems and quantum graphs are explained. Firstly, a boundary value transmission problem with one point of interaction is considered and realized as a boundary value problem on a metric graph (two-star graph). The self-adjointness of the corresponding operators is discussed in these two settings. Secondly, a two-star graph with general self-adjoint vertex conditions is considered and treated as a transmission problem. To this end, a new special inner product which makes the quantum two-star graph self-adjoint in a general sense is defined. It is shown that the usual self-adjointness of a two-star graph can be obtained as a special case.