We consider two types of convolutions (* and ★) 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 derivation with respect to the *-convolution are investigated. We also present conditions under which the *-convolution is positive-definite with respect to the ★-convolution.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 11, pp. 1547–1567, November, 2012.
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Finkel’shtein, D.L. On convolutions on configuration spaces. I. Spaces of finite configurations. Ukr Math J 64, 1752–1775 (2013). https://doi.org/10.1007/s11253-013-0749-y
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DOI: https://doi.org/10.1007/s11253-013-0749-y