ON THE ASYMPTOTIC BEHAVIOUR OF THE UNSTABLE BLOCH EIGENVALUES OF A POLYHARMONIC MATRIX OPERATOR
REPORTS ON MATHEMATICAL PHYSICS, vol.96, no.1, pp.55-74, 2025 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 96 Issue: 1
- Publication Date: 2025
- Doi Number: 10.1016/s0034-4877(25)00054-0
- Journal Name: REPORTS ON MATHEMATICAL PHYSICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, MathSciNet, zbMATH
- Page Numbers: pp.55-74
- Keywords: perturbation theory, system of polyharmonic operators, eigenvalue, asymptotic, resonance domain
- Dokuz Eylül University Affiliated: Yes
Abstract
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.