Resolvent expansions for self‐adjoint operators via boundary triplets
Resolvent expansions for self‐adjoint operators via boundary triplets
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DOI：
10.1112/blms.12706
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发表时间：
2021-10
影响因子：
0.9
通讯作者：
Y. Latushkin;Selim Sukhtaiev
中科院分区：
文献类型：
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作者：
Y. Latushkin;Selim Sukhtaiev
在本文中，我们发展了自伴算子的扰动理论的某些方面，它们的域有小的变化。我们使用边界三元组的抽象理论来量化这种扰动，并给出相应自伴算子的预解式、谱投影和离散特征值的二阶渐近分析。特别是，我们推导出明确的公式的第一变分和Hessian的特征值曲线从一个离散的特征值的未扰动的操作。给出了矩阵值Robin Laplacian和更一般的Robin型自伴扩张的应用。
In this paper, we develop certain aspects of perturbation theory for self‐adjoint operators subject to small variations of their domains. We use the abstract theory of boundary triplets to quantify such perturbations and give the second‐order asymptotic analysis for resolvents, spectral projections, and discrete eigenvalues of the corresponding self‐adjoint operators. In particular, we derive explicit formulas for the first variation and the Hessian of the eigenvalue curves bifurcating from a discrete eigenvalue of an unperturbed operator. An application is given to a matrix valued Robin Laplacian and more general Robin‐type self‐adjoint extensions.