Absence of singular continuous spectrum for perturbed discrete Schrödinger operators

Abstract

We show that the spectral measure of discrete Schrödinger operators $(Hu)(n)=u(n+1)+u(n-1)+V(n)u(n)$ does not have singular continuous component if the potential $V(n)=O(n^{-1})$.

References in corpus (5)

• Criteria for embedded eigenvalues for discrete Schrödinger operators
• Spectral Properties of Schrödinger Operators with Decaying Potentials
• Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators
• Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique
• Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators

Cited by in corpus (8)

• Criteria for embedded eigenvalues for discrete Schrödinger operators
• Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators
• Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators
• The asymptotical behaviour of embedded eigenvalues for perturbed periodic operators
• Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators
• Revisiting the Christ-Kiselev's multi-linear operator technique and its applications to Schrödinger operators
• Limiting absorption principle for discrete Schr{ö}dinger operators with a Wigner-von Neumann potential and a slowly decaying potential
• Bands of pure a.c. spectrum for lattice Schr{ö}dinger operators with a more general long range condition. Part I