Resolvent expansions for self‐adjoint operators via boundary triplets

In this paper, we develop certain aspects of perturbation theory for self‐adjoint operators subject to small variations of their domains. We use the 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.