  We prove that the ground state eigenfunction for symmetric stable processes
of order $\alpha\in (0, 2)$ killed upon leaving the interval $(-1, 1)$ is
concave on $(-{1/2}, {1/2})$. We call this property "mid--concavity." A similar
statement holds for rectangles in $\R^d$, $d>1$. These result follow from
similar results for finite dimensional distributions of Brownian motion and
subordination.
