A_{Theta} = A_0 + B Theta B*,

where A_0 is a distinguished self-adjoint extension and Theta is a self-adjoint linear relation in C^d. The perturbation is singular in the sense that it does not belong to the underlying Hilbert space but is form bounded with respect to A_0, i.e. it belongs to H_{-1}(A_0). The construction of a boundary triple and compatible boundary pair for the symmetric operator ensure that the perturbation is well-defined and self-adjoint extensions are in a one-to-one correspondence with self-adjoint relations Theta.

As an example, self-adjoint extensions of the classical symmetric Jacobi differential equation (which has two limit-circle endpoints) are obtained and their spectra is analyzed with tools both from the theory of boundary triples and perturbation theory.