  We prove that, in (2+1) dimensions, the S-wave phase shift, $ \delta_0(k)$, k
being the c.m. momentum, vanishes as either $\delta_0 \to {c\over \ln (k/m)} or
\delta_0 \to O(k^2)$ as $k\to 0$. The constant $c$ is universal and $c=\pi/2$.
This result is established first in the framework of the Schr\"odinger equation
for a large class of potentials, second for a massive field theory from proved
analyticity and unitarity, and, finally, we look at perturbation theory in
$\phi_3^4$ and study its relation to our non-perturbative result. The
remarkable fact here is that in n-th order the perturbative amplitude diverges
like $(\ln k)^n$ as $k\to 0$, while the full amplitude vanishes as $(\ln
k)^{-1}$. We show how these two facts can be reconciled.
