On convolutions on configuration spaces. I. Spaces of finite configurations - Finkelshtein, D. L. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We consider two types of convolutions ($*$ and $\star$) of functions on spaces of finite configurations (finite subsets of a phase space) and study some of their properties. A relationship between the $*$-convolution and the convolution of measures on spaces of finite configurations is described. Properties of the operators of multiplication and differentiation with respect to the $*$-convolution are investigated. We also present conditions under which the $*$-convolution is positive definite with respect to the $\star$-convolution.