  We consider two types of convolutions ($\ast$ and $\star$) of functions on
spaces of finite configurations (finite subsets of a phase space), and some
their properties are studied. A connection of the $\ast$-convolution with the
convolution of measures on spaces of finite configurations is shown. Properties
of multiplication and derivative operators with respect to the
$\ast$-convolution are discovered. We present also conditions when the
$\ast$-convolution will be positive definite with respect to the
$\star$-convolution.
