论文标题
在带有$δ'$的字符串上 - 例如质量密度的扰动
On spectrum of strings with $δ'$-like perturbations of mass density
论文作者
论文摘要
我们研究了具有一般边界条件的sturm-liouville操作员的特征值和边界价值问题的特征值的渐近行为，而所谓的$δ” $扰乱了重量函数，例如序列$ \ varepsilon^{-2} h（x/\ varepsilon）$。特征值问题被实现为一个非自我伴侣矩阵操作员的家族，该家族在同一希尔伯特空间上作用，并建立了该家族的规范分辨率融合。我们还证明了扰动光谱的Hausdorff收敛。
We study the asymptotic behaviour of eigenvalues and eigenfunctions of a boundary value problem for the Sturm-Liouville operator with general boundary conditions and the weight function perturbed by the so-called $δ'$-like sequence $\varepsilon^{-2}h(x/\varepsilon)$. The eigenvalue problem is realized as a family of non-self-adjoint matrix operators acting on the same Hilbert space and the norm resolvent convergence of this family is established. We also prove the Hausdorff convergence of the perturbed spectra.
