Before revision:  On the other hand, much less is known in the multivariate case, where the domain of the filter is  in \mathbb R^d instead of \mathbb R. The only available result in this setting ~\mbox{%DIFAUXCMD Munch2016  topological spaces and cannot be used as is for finite metric spaces representing data, such as point clouds and distance matrices.
After revision:  On the other hand, much less is known in the multivariate case, where the domain of the filter is in this setting ~\mbox{%DIFAUXCMD Munch2016 topological spaces and cannot be used as is for finite metric spaces representing data, such as point clouds and distance matrices.