a linear relation $T\in \C(\cH)$ and for any $\l \in \bC$ we let $$\gN_\l (T):=\ker (T^*-\l)\,(=\cH\ominus \ran (T-\ov\l)), \quad \hat
\gN_{\l}(T):=\{\{f,\l f\}:f\in \gN_{\l }(T)\}\subset T^*.$$ If $\ov\l\in\hat\rho (T)$, then $\gN_\l (T)$ is a defect subspace of $T$. Recall also the following definition.

\[def2.0\] A holomorphic operator function $\Phi (\cd):\bC\setminus\bR\to [\cH]$ is called a Nevanlinna function if $\im\, z\cd \im \Phi (z)\geq 0 $ and $\Phi ^*(z)=
\Phi (\ov z), \; z\in\bC\setminus\bR$.

Operator pairs 
---------------

Let $\cK,\cH_0,\cH_1$ be Hilbert spaces. A pair of operators $C_j\in
[\cH_j,\cK],  \;j\in\{0,1\}$ is called admissible if the range of the operator $$\label{2.1}
C=(C_0:\,C_1):\cH_0\oplus\cH_1\to\cK$$ coincides with $\cK$. In the sequel all pairs are admissible unless otherwise stated.

Two pairs $(C_0^{(j)}:\,C_1^{(j)}):
\cH_0\oplus\cH_1\to\cK_j, \; j\in\{1,2\}$ will be called equivalent if $C_0^{(2)}=XC_0^{(1)}$ and $C_1^{(2)}=XC_1^{(1)}$ with some isomorphism $X\in
[\cK_1,\cK_2]$.

It is clear that the set of all operator pairs falls into nonintersecting classes of equivalent pairs. Moreover, the equality $$\label{2.2}
\t=\{(C_0,C_1);\cK\}:=\{\{h_0, h_1\}\in\cH_0\oplus\cH_1:\, C_0h_0+C_1h_1=0\}$$ establishes a bijective correspondence between all linear relations $\t\in\CA$ and all equivalence classes of operator pairs . Therefore in the sequel we identify (by means of ) a linear relation $\t\in\CA$ and the corresponding class of equivalent operator pairs $C_j\in [\cH_j,\cK], \;
j\in \{0,1\}$.

Next recall some 