Kang Lyu

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20232026

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math-ph2026

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 $ℓ^{2} (N)$ with a self-adjoint boundary co…

math-ph2024

On the perturbed periodic Schrödinger operators with separate resonant embedded eigenvalues

Kang Lyu, Chuanfu Yang

In this paper, we consider Schrödinger operators on $L^{2} (0, \infty)$ given by \begin{align} Hu=(H_0+V)u=-u^{\prime\prime}+V_0u+Vu,\nonumber \end{align} where $V_{0}$ is real, $1$ -peri…

math-ph2024

Sharp spectral transition for embedded eigenvalues of perturbed periodic Dirac operators

Kang Lyu, Chuanfu Yang

We consider the Dirac equation on $L^{2} (R) \oplus L^{2} (R)$ \begin{align} Ly= \begin{pmatrix} 0&-1 1&0 \end{pmatrix} \begin{pmatrix} y_1 y_2 \end{pmatrix}'+ \begin{pm…