Boundary triples and Weyl functions for singular perturbations of self-adjoint operators

Given the symmetric operator $A_N$ obtained by restricting the self-adjoint operator $A$ to $N$, a linear dense set, closed with respect to the graph norm, we determine a convenient boundary triple for the adjoint $A_N^{\ast }$ and the corresponding Weyl function. These objects provide us with the self-adjoint extensions of $A_N$ and their resolvents.