we describe all such conditions in the compact form. These results are generalizations of the known results by Rofe-Beketov on regular differential operators. We characterize also all maximal dissipative and accumulative separated boundary conditions, which exist for arbitrary (not necessarily Hamiltonian) definite canonical systems.
address: |
    Department of Calculus\
    Lugans’k National University\
    2 Oboronna, Lugans’k, 91011\
    Ukraine
author:
- Vadim Mogilevskii
title: 'Boundary relations and boundary conditions for general (not necessarily definite) canonical systems with possibly unequal deficiency indices'
---

Introduction
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Assume that $\gH$ is a Hilbert space, $A$ is a closed symmetric linear relation in $\gH$ and $A^*$ is the adjoint linear relation of $A$. Moreover, denote by $[\gH_1, \gH_2]$ the set of all bounded operators between $\gH_1$ and $\gH_2$ and let $[\gH]=[\gH, \gH]$.

Recall [@GorGor; @Mal92] that a triplet $\Pi=\bt $, where $\cH$ is an auxiliary Hilbert space and $\G_0,\G_1: A^*\to \cH$ are (boundary) linear maps, is called a boundary triplet for $A^*$ if the map $\G:=(\G_0\;\;\G_1)^\top:A^*\to \cH\oplus\cH$ is surjective and the following ”abstract Green’s identity” holds $$\label{1.1}
(f',g)-(f,g')=(\G_1  \hat f, \G_0 \hat g)-(\G_0\hat f,\G_1\hat g), \quad \hat
f=\{f,f'\},\;\hat g=\{g,g'\}\in  A^*.$$

In [@DM91; @Mal92] an abstract Weyl function $M_\Pi(\l)$ was associated with a boundary triplet $\Pi$. This 