  Prompted by modern technologies in data acquisition, the statistical analysis
of spatially distributed function-valued quantities has attracted a lot of
attention in recent years. In particular, combinations of functional variables
and spatial point processes yield a highly challenging instance of such modern
spatial data applications. Indeed, the analysis of spatial random point
configurations, where the point attributes themselves are functions rather than
scalar-valued quantities, is just in its infancy, and extensions to
function-valued quantities still remain limited. In this view, we extend
current existing first- and second-order summary characteristics for
real-valued point attributes to the case where in addition to every spatial
point location a set of distinct function-valued quantities are available.
Providing a flexible treatment of more complex point process scenarios, we
build a framework to consider points with multivariate function-valued marks,
and develop sets of different cross-function (cross-type and also
multi-function cross-type) versions of summary characteristics that allow for
the analysis of highly demanding modern spatial point process scenarios. We
consider estimators of the theoretical tools and analyse their behaviour
through a simulation study and two real data applications.
