direct sum of (the graph of) the operator $G=(G_0\;\;G_1)^\top$ and $ \mul\G$.

The multivalued part $\mul \G$ which is a linear relation from $\cH_0$ to $\cH_1$ is of importance in our considerations. If $\mul \G$ is the operator, then the corresponding Weyl family $M_+(\l)$ is the holomorphic operator function with values in $[\cH_0, \cH_1]$, which admits the block representation by means of the Weyl function $M_{\Pi_\G +} (\l)$ of the boundary triplet $\Pi_\G$ and $\mul \G $. In the case $\cH_0=\cH_1=:\cH$ one has also $\cK_0=\cK_1=:\cK$ and the mentioned representation of $M(\l)$ is $$\begin{gathered}
\label{1.7}
M(\l)=\begin{pmatrix} M_{\Pi_\G}(\l) & F \cr F^* & F'\end{pmatrix}:
\cK\oplus\cK^\perp\to \cK\oplus\cK^\perp,\end{gathered}$$ where $F$ and $F'$ are the operators defined in terms of $\mul\G$. The equality shows that $M(\l)$ is a Nevanlinna function and $M_{\Pi_\G}(\l)$ is the uniformly strict part of $M(\l)$.

Note that for the boundary relation $\BR$ with $\dim\cH_0 <\infty$ the equalities $$\begin{gathered}
\dim\cH_0=n_+(A)+\dim (\mul\G), \qquad \dim\cH_1=n_-(A)+\dim (\mul\G)\end{gathered}$$ are valid (c.f. ), so that $n_-(A)\leq n_+(A)<\infty$. At the same time in the case of unequal deficiency indices $n_+(A)\neq n_-(A)$ each boundary relation $\G:\gH^2\to \cH^2$ for $A^*$ in the sense of [@DM06] satisfies the equality $\dim \cH=\infty$ (see [@DM09 Proposition 3.2]). This assertion shows that in the 