On convolutions on configuration spaces. I. Spaces of finite configurations
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.
English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 11, pp 1752-1775.
Citation Example: Finkelshtein D. L. On convolutions on configuration spaces. I. Spaces of finite configurations // Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1547-1567.