A note on the asymptotic and threshold behaviour of discrete eigenvalues inside the spectral gaps of the difference operator with a periodic potential

DOI10.1155/2018/4696790zbMath1403.39015OpenAlexW2793948280MaRDI QIDQ1629216

Josiah Mushanyu, Gift Muchatibaya

Publication date: 11 December 2018

Published in: Advances in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2018/4696790

zbMATH Keywords

Birman-Schwinger principleperturbed difference operatorTitchmarsh-Weyl function theory

Mathematics Subject Classification ID

Stability theory for difference equations (39A30) Applications of difference equations (39A60)

Related Items (1)

The discrete \(p\)-Schrödinger equations under the mixed boundary conditions on networks

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The discrete spectrum in the gaps of a second-order perturbed periodic operator
• On the existence of eigenvalues of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H)
• Eigenvalue branches of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H)
• On the bound state of Schrödinger operators in one dimension
• Critical coupling constants and eigenvalue asymptotics of perturbed periodic Sturm-Liouville operators
• Perturbation of operators and approximation of spectrum
• Spectral theory of difference operators with almost constant coefficients
• Effect of Free Ends on the Vibration Frequencies of One-Dimensional Lattices
• Half-Bound States and Levinson’s Theorem for Discrete Systems
• On the asymptotic form of the Titchmarsh-Weylm-coefficient†
• Coupling constant thresholds of perturbed periodic Hamiltonians

This page was built for publication: A note on the asymptotic and threshold behaviour of discrete eigenvalues inside the spectral gaps of the difference operator with a periodic potential