\quad \{\wt y, \wt f\} \in
\Tma \label{1.23}\end{gathered}$$ (here $\G_{0b}, \;\G_{1b}$ and $\hat\G_b$ are taken from ). In the case of the regular system one can put $\cH= H\oplus\hat H \oplus H$ and $$\begin{gathered}
\G_0 \{\wt y, \wt f\}=\{ y_0(a),\, \tfrac i {\sqrt 2} (\hat y(a)-\hat
y(b)),\, y_0(b) \}(\in H\oplus\hat H \oplus H),\qquad\qquad\qquad\quad\label{1.24} \\
\G_1 \{\wt y, \wt f\}= \{ y_1(a),\, \tfrac 1 {\sqrt 2}(\hat y(a)+\hat
y(b)),\,-y_1(b) \}(\in H\oplus\hat H \oplus H),\quad \{\wt y, \wt f\} \in \Tma.
\label{1.25}\end{gathered}$$ The boundary triplet $\bt$ defined via and is similar to that introduced, in fact, by Rofe-Beketov [@Rof69] for regular differential operators of a higher order. Observe also that other constructions of a boundary triplet for $\Tma$ in the case of the definite system can be found in [@BHSW10].

The decomposing boundary triplet , enables us to describe maximal dissipative, maximal accumulative and self-adjoint boundary conditions, which define in terms of boundary values the extensions $\wt A\supset \Tmi$ of the corresponding class. As a consequence we obtain the known description of self-adjoint boundary conditions, given in [@Atk; @GK; @Orc] for regular definite systems and in [@Kra89] for definite Hamiltonian systems with the regular endpoint $a$.

Finally by using the concept of a 