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arXiv · 1210.5121

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

Dmitri Finkelshtein
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Abstract

We consider two types of convolutions ($\ast$ and $\star$) of functions on spaces of finite configurations (finite subsets of a phase space), and some their properties are studied. A connection of the $\ast$-convolution with the convolution of measures on spaces of finite configurations is shown. Properties of multiplication and derivative operators with respect to the $\ast$-convolution are discovered. We present also conditions when the $\ast$-convolution will be positive definite with respect to the $\star$-convolution.

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Dmitri Finkelshtein. 2012-10-18. Towards on convolutions on configuration spaces. I. Spaces of finite configurations. https://arxiv.org/abs/1210.5121

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