6 papers
Optimal bounds for embedded eigenvalues of one-dimensional discrete Schrödinger operators with decaying potentials
Jifeng Chu, Wencai Liu, Kang Lyu
In this paper, we consider one-dimensional discrete Schrödinger operators \begin{align} Hu(n)=(Δ+V)u(n)\nonumber \end{align} on with a self-adjoint boundary co…
Weak separability and partial Fermi isospectrality of discrete periodic Schrödinger operators
Jifeng Chu, Kang Lyu, Chuan-Fu Yang
In this paper, we consider the discrete periodic Schrödinger operators on , where is -periodic with $Γ=q_1 \mathbb{Z}\oplus q_2\mathbb{Z}\oplus\cdots\oplus q_d\m…
On the perturbed periodic Schrödinger operators with separate resonant embedded eigenvalues
Kang Lyu, Chuanfu Yang
In this paper, we consider Schrödinger operators on given by \begin{align} Hu=(H_0+V)u=-u^{\prime\prime}+V_0u+Vu,\nonumber \end{align} where is real, -peri…
Sharp spectral transition for embedded eigenvalues of perturbed periodic Dirac operators
Kang Lyu, Chuanfu Yang
We consider the Dirac equation on \begin{align} Ly= \begin{pmatrix} 0&-1 1&0 \end{pmatrix} \begin{pmatrix} y_1 y_2 \end{pmatrix}'+ \begin{pm…
Sharp bound for embedded eigenvalues of Dirac operators with decaying potentials
Vishwam Khapre, Kang Lyu, Andrew Yu
We study eigenvalues of the Dirac operator with canonical form \begin{equation} L_{p,q} \begin{pmatrix} u \\ v \end{pmatrix}= \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}\frac{d}{…
One dimensional discrete Schrödinger operators with resonant embedded eigenvalues
Wencai Liu, Kang Lyu
In this paper, we introduce a new family of functions to construct Schrödinger operators with embedded eigenvalues. This particularly allows us to construct discrete Schrödinger op…