2021/10/14 by Yuri Latushkin, Latushkin, Yuri, Selim Sukhtaiev +1
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #Advanced Mathematical Modeling in Engineering #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2110.07434
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, 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.