Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators

Abstract

In this paper, we consider the perturbed Stark operator \begin{equation*} Hu=H_0u+qu=-u^{\prime\prime}-xu+qu, \end{equation*} where $q$ is the power-decaying perturbation. The criteria for $q$ such that $H=H_0+q$ has at most one eigenvalue (finitely many, infinitely many eigenvalues) are obtained. All the results are quantitative and are generalized to the perturbed Stark type operator.

arXiv commentJ. Funct. Anal. to appear

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Cited by in corpus (9)

• Criteria for embedded eigenvalues for discrete Schrödinger operators
• Topics on Fermi varieties of discrete periodic Schrödinger operators
• Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators
• Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian
• 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
• The Dirichlet problem for perturbed Stark operators in the half-line
• Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators
• One-dimensional Stark operators in the half-line