A\subset A^*$ and conversely each such an extension $\wt A$ admits a unique representation . Moreover, the extension $\wt A$ is maximal dissipative, maximal accumulative or self-adjoint if and only if the operator pair $\{(C_0,C_1);\cK\}$ belongs to one of the special classes introduced in [@Mog06.1].

It turns out that each boundary triplet $\Pi=\bta$ satisfies the relation $$\begin{gathered}
\label{1.5a}
\dim\cH_1=n_-(A)\leq n_+(A)=\dim\cH_0\end{gathered}$$ and, therefore, it is applicable to symmetric relations $A$ with unequal deficiency indices. Clearly, in the case $\cH_0=\cH_1=:\cH$ such a triplet $\Pi
$ and the corresponding Weyl function $M_\Pi(\l)$ turn into the similar objects in the sense of [@GorGor; @Mal92].

In [@DM95] the notion of a boundary triplet $\Pi=\bt$ for $A^*$ has been extended to the case where the corresponding Weyl function $M_\Pi(\l)$ is a (not necessarily uniformly strict) Nevanlinna function such that $0\notin\sigma_p(\im M(i))$. Next, the concepts of a boundary relation and its Weyl family which generalize the above notions of a boundary triplet and its Weyl function were introduced in [@DM06]. According to [@DM06] a boundary relation for $A^*$ is a (possibly multivalued) linear map $\G:=(\G_0\;\;\G_1)^\top:\gH^2\to \cH\oplus\cH$ such that $\dom\G$ is dense in $A^*$, the Green’s identity holds and a certain maximality condition is satisfied. The Weyl function 