On convolutions on configuration spaces. I. Spaces of finite configurations

  • D. L. Finkelshtein Iн-т математики НАН України, Київ


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.
How to Cite
Finkelshtein, D. L. “On Convolutions on Configuration Spaces. I. Spaces of Finite Configurations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 11, Nov. 2012, pp. 1547-6, https://umj.imath.kiev.ua/index.php/umj/article/view/2680.
Research articles