  In this paper, some theoretical aspects will be addressed for the asymptotic
preserving DG-IMEX schemes recently proposed in [J. Jang, F. Li, J.-M. Qiu and
T. Xiong, submitted, arxiv:1306.0227] for kinetic transport equations under a
diffusive scaling. We will focus on the methods that are based on discontinuous
Galerkin (DG) spatial discretizations with the $P^k$ polynomial space and a
first order IMEX temporal discretization, and apply them to two linear models:
the telegraph equation and the one-group transport equation in slab geometry.
In particular, we will establish uniform numerical stability with respect to
Knudsen number $\varepsilon$ using energy methods, as well as error estimates
for any given $\varepsilon$. When $\varepsilon\rightarrow 0$, a rigorous
asymptotic analysis of the schemes is also obtained. Though the methods and the
analysis are presented for one dimension in space, they can be generalized to
higher dimensions directly.
