  In this paper, we study the equation $\mathcal{L} u=0$ in $\mathbb{R}^N$,
where $\mathcal{L}$ belongs to a general class of nonlocal linear operators
which may be anisotropic and nonsymmetric. We classify distributional solutions
of this equation, thereby extending and generalizing recent Liouville type
theorems in the case where $\mathcal{L}= (-\Delta)^s$, $s \in (0,1)$ is the
classical fractional Laplacian.
