The asymptotical behaviour of embedded eigenvalues for perturbed periodic operators

Abstract

Let $H_0$ be a periodic operator on ${\mathbb{R}}^{+}$(or periodic Jacobi operator on $\mathbb{N}$). It is known that the absolutely continuous spectrum of $H_0$ is consisted of spectral bands $\cup [{\alpha }_l,{\beta }_l]$. Under the assumption that ${\mathrm{limsup}}_{x\to \infty }x|V(x)|<\infty$ (${\mathrm{limsup}}_{n\to \infty }n|V(n)|<\infty$), the asymptotical behaviour of embedded eigenvalues approaching to the spectral boundary is established.

References in corpus (3)

• Criteria for embedded eigenvalues for discrete Schrödinger operators
• Absence of singular continuous spectrum for perturbed discrete Schrödinger operators
• Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators

Cited by in corpus (4)

• Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators
• Revisiting the Christ-Kiselev's multi-linear operator technique and its applications to Schrödinger operators
• Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators
• Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators