@article{Finkelshtein_2012, title={On convolutions on configuration spaces. I. Spaces of finite configurations}, volume={64}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/2680}, abstractNote={We consider two types of convolutions ($\ast$ 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 $\ast$-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 $\ast$-convolution are investigated. We also present conditions under which the $\ast$-convolution is positive definite with respect to the $\star$-convolution.}, number={11}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={FinkelshteinD. L.}, year={2012}, month={Nov.}, pages={1547-1567} }