A class of Schrodinger operators with decaying oscillatory potentials

Abstract

We discuss Schrödinger operators on a half-line with decaying oscillatory potentials, such as products of an almost periodic function and a decaying function. We provide sufficient conditions for preservation of absolutely continuous spectrum and give bounds on the Hausdorff dimension of the singular part of the spectral measure. We also discuss the analogs for orthogonal polynomials on the real line and unit circle.

arXiv comment18 pages

References in corpus (1)

• Orthogonal Polynomials with Recursion Coefficients of Generalized Bounded Variation

Cited by in corpus (8)

• Criteria for embedded eigenvalues for discrete Schrödinger operators
• Bifurcations in asymptotically autonomous Hamiltonian systems under oscillatory perturbations
• 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
• Damped perturbations of systems with centre-saddle bifurcation
• Resonances in asymptotically autonomous systems with a decaying chirped-frequency excitation
• Limiting absorption principle for discrete Schr{ö}dinger operators with a Wigner-von Neumann potential and a slowly decaying potential
• Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators