Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators
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DOI: 10.1002/mana.201800517
Abstract: For perturbed Stark operators $Hu=-u^{\prime\prime}-xu+qu$, the author has proved that $\limsup_{x\to \infty}{x}^{\frac{1}{2}}|q(x)|$ must be larger than $\frac{1}{\sqrt{2}}N^{\frac{1}{2}}$ in order to create $N$ linearly independent eigensolutions in $L^2(\mathbb{R}^+)$. In this paper, we apply generalized Wigner-von Neumann… read more here.
Keywords: sharp bounds; perturbed stark; finitely many; embedded eigenvalues ... See more keywords
Criteria for Embedded Eigenvalues for Discrete Schrödinger Operators
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DOI: 10.1093/imrn/rnz262
Abstract: In this paper, we consider discrete Schrödinger operators of the form, $$\begin{equation*} (Hu)(n) = u({n+1})+u({n-1})+V(n)u(n). \end{equation*}$$We view $H$ as a perturbation of the free operator $H_0$, where $(H_0u)(n)= u({n+1})+u({n-1})$. For $H_0$ (no perturbation), $\sigma _{\textrm{ess}}(H_0)=\sigma… read more here.
Keywords: embedded eigenvalues; dinger operators; discrete schr; criteria embedded ... See more keywords