论文标题
无限laplacian的复杂扰动的尖锐光谱边界
Sharp spectral bounds for complex perturbations of the indefinite Laplacian
论文作者
论文摘要
我们得出了无限laplacian在实际线路上的复杂扰动的特征值的定量界限。我们的结果即使是对实现的潜力，我们的结果也大大提高了现有结果。对于$ l^1 $ - 潜在的，我们获得了适合嵌入特征值的最佳光谱外壳，而我们对$ l^p $ - 电位的结果在[1，\ infty）$ in [1，\ infty）$中$ p \ in All $ p \ in [1，p $ p \ in frusted oteranvalues的想象中均产生了鲜明的频谱界限。通过明确的例子证明了结果的清晰度。
We derive quantitative bounds for eigenvalues of complex perturbations of the indefinite Laplacian on the real line. Our results substantially improve existing results even for real-valued potentials. For $L^1$-potentials, we obtain optimal spectral enclosures which accommodate also embedded eigenvalues, while our result for $L^p$-potentials yield sharp spectral bounds on the imaginary parts of eigenvalues of the perturbed operator for all $p\in[1,\infty)$. The sharpness of the results are demonstrated by means of explicit examples.
