Boundary value space associated with a given Weyl function
Let S be a symmetric linear relation in the Pontyagin space (K, [., .]) and let Π = (H,Γ0,Γ1) be the corresponding boundary triple. We prove that the corresponding Weyl function Q satisfies Q ∈ Nκ(H). Conversely, for regular Q ∈ Nκ(H), we find linear relation S ( A, where A is representing self-adjoint linear relation of Q, and we prove that Q is the Weyl function of the relation S. We also prove  = kerΓ1, where  is the representing relation of the Q̂ := −Q−1. In addition, if we assume that the derivative at infinity Q ′ (∞) := lim z→∞ zQ(z) is a boundedly invertible operator then we are able to decompose A,  and S in terms of S, i.e. we express relation matrices of A,  and S in terms of S, which is a bounded operator in this case.