all proper extensions $\wt A\in\exa$ is parameterized by linear relations (operator pairs) $\t=\{(C_0,C_1);\cK\}$. More precisely, the mapping $$\label{2.5}
\t\to  A_\t :=\{ \hat f\in A^*:\{\G_0  \hat f,\G_1 \hat f \}\in \t\}$$ establishes a bijective correspondence between the linear relations $\t\in\CA$ and the extensions $ \wt A= A_\t\in\exa$. If $\t$ is given as an operator pair $\t=\{(C_0,C_1);\cK \}$, then $A_\t$ can be represented in the form of an abstract boundary condition: $$\label{2.5a}
A_\t=\{\hat f\in A^*: C_0\G_0 \hat f+C_1\G_1\hat  f=0 \}$$

3\) the extension $ A_\t$ is maximal dissipative, maximal accumulative, maximal symmetric or self-adjoint if and only if $\t$ belongs to the class $Dis,\; Ac,\; Sym$ or $Self (\cH_0,\cH_1)$ respectively;

4\) The equality $$\label{2.6}
A_0:=\ker \G_0=\{\hat f\in A^*:\G_0 \hat f=0\}$$ defines the maximal symmetric extension $A_0\in\exa$ such that $n_-(A_0)=0$.

It turns out that for every $\l\in\bC_+\;(z\in\bC_-)$ the map $\G_0\up \hat
\gN_\l (A)$ (resp $P_1\G_0\up \hat \gN_z (A)$) is an isomorphism. This makes it possible to introduce the $\g$-fields $\g_{\Pi +}(\cdot):\Bbb
C_+\to[\cH_0,\gH], \; \; \g_{\Pi -}(\cdot):\Bbb C_-\to[\cH_1,\gH]$ and the Weyl functions $M_{\Pi +}(\cdot):\bC_+\to [\cH_0,\cH_1], \;\; M_{\Pi
-}(\cdot):\bC_-\to [\cH_1,\cH_0]$ by $$\begin{gathered}
\g_{\Pi +} (\l)=\pi_1(\G_0\up\hat \gN_\l (A))^{-1}, \;\;\l\in\Bbb C_+;\quad
\g_{\Pi -} (z)=\pi_1(P_1\G_0\up\hat\gN_z (A))^{-1}, \;\; z\in\Bbb C_-,
\label{2.7}\\
\G_1 \up \hat\gN_\l (A)=M_{\Pi +}(\l)\G_0 \up \hat\gN_\l (A),\quad 