Ordinary boundary triple associated with a given function Q ∈
Abstract: Let S be a symmetric linear relation in the Pontryagin space (K, [., .]) of index κ, let Π = (H,Γ0,Γ1) be an ordinary boundary triple for the relation S, and let Q be the Weyl function corresponding to S and Π. By means of a version of the Krein formula in Pontryagin space, we prove  = kerΓ1, where  is the representing relation of Q̂ := −Q−1 ∈ Nκ(H). For regular function Q ∈ Nκ(H), with representing relation A, we find symmetric relation S, {0} ⊆ S ( A, and the boundary triple Π such that Q is the Weyl function corresponding to S and Π. Then we assume that the derivative at infinity Q ′ (∞) := lim z→∞ zQ(z) is a boundedly invertible operator. That enables us to express