function is defined for all $\l\in\CR$ by the equality $$\begin{gathered}
\label{1.2}
\G_1\{f_\l,\l f_\l\}=M_\Pi(\l)\G_0\{f_\l,\l f_\l\}, \quad f_\l\in\ker (A^*-\l).\end{gathered}$$ It turns out that $M(\l)$ is a Nevanlinna $[\cH]$-valued function, i.e., $M(\l)$ is holomorphic on $\CR$, $M^*(\l)=M(\ov\l)$ and $\im\l\cd \im M(\l)\geq
0, \; \l\in\CR $. Moreover, the Nevanlinna function $M(\l)$ is uniformly strict, that is $0\in\rho (\im M(\l)), \; \l\in\CR$.

By choosing a suitable boundary triplet for a concrete problem one can parametrize various classes of extensions $\wt A\supset A$ in the most convenient form. Moreover, the Weyl function enables to characterize spectra of extensions $\wt A$ in the similar way as classical $m$-functions in the spectral theory of Sturm-Liouville operators and Jacobi matrices. These and other reasons made a boundary triplet and the corresponding Weyl function the convenient tools in the extension theory of symmetric operators (linear relations) and its applications (see [@GorGor; @DM91; @Mal92] and references therein). At the same time the theory of boundary triplets and their Weyl functions was developed in [@GorGor; @DM91; @Mal92] only for symmetric relations $A$ with equal deficiency indices $n_+(A)=n_-(A)$.

To cover the case $n_+(A)\neq n_-(A)$ we generalized in [@Mog06.2] definition of a boundary triplet as follows. Assume that $\cH_0$ is a Hilbert space, $\cH_1$ 