TY - JOUR
AU - D. L. Finkelshtein
PY - 2012/11/25
Y2 - 2020/12/05
TI - On convolutions on configuration spaces. I. Spaces of finite configurations
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 64
IS - 11
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/2680
AB - 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.
ER -