  Streamer ionization fronts are pulled fronts propagating into a linearly
unstable state; the spatial decay of the initial condition of a planar front
selects dynamically one specific long time attractor out of a continuous
family. A transverse stability analysis has to take these features into
account. In this paper we introduce a framework for this transverse stability
analysis, involving stable and unstable manifolds in a weighted space. Within
this framework, a numerical dynamical systems method for the calculation of the
dispersion relation as an eigenvalue problem is defined and dispersion curves
for different values of the electron diffusion constant and of the electric
field ahead of the front are derived. Numerical solutions of the initial value
problem confirm the eigenvalue calculations. The numerical work is complemented
with analytical expressions for the dispersion relation in the limit of small
and large wave numbers and with a fit formula for intermediate wave numbers.
This empirical fit supports the conjecture that the smallest unstable wave
length of the Laplacian instability is proportional to the diffusion length
that characterizes the leading edge of the pulled ionization front.
