ON THE ASYMPTOTIC BEHAVIOUR OF THE UNSTABLE BLOCH EIGENVALUES OF A POLYHARMONIC MATRIX OPERATOR

KARAKILIÇ S., ÖZCAN S., Akduman S.

REPORTS ON MATHEMATICAL PHYSICS, cilt.96, sa.1, ss.55-74, 2025 (SCI-Expanded, Scopus) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 96 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1016/s0034-4877(25)00054-0
  • Dergi Adı: REPORTS ON MATHEMATICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.55-74
  • Anahtar Kelimeler: perturbation theory, system of polyharmonic operators, eigenvalue, asymptotic, resonance domain
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

We explore the asymptotic behaviour of the so-called unstable Bloch eigenvalues of the polyharmonic matrix operator (-Delta)(l) +V(x) with (1)/(2) < l < 1, in the single resonance domain which is a subset of resonance domain - the set of eigenvalues situated close to the diffraction hyper planes. The single resonance domain approaches full measure asymptotically across the entire resonance domain. In our analysis, we discover a significant trend: as energy levels increase, the eigenvalues are related to those of a Sturm-Liouville operator.