  This paper focuses on the use of the theory of Reproducing Kernel Hilbert
Spaces in the statistical analysis of replicated point processes. We show that
spatial point processes can be observed as random variables in a Reproducing
Kernel Hilbert Space and, as a result, methodological and theoretical results
for statistical analysis in these spaces can be applied to them. In particular
and by way of illustration, we show how we can use the proposed methodology to
identify differences between several classes of replicate point patterns using
the MBox and MANOVA tests, and to classify a new observation, using
Discriminant Functions.
