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arXiv · 2312.03537

Analysis on the cone of discrete Radon measures

Dmitri Finkelshtein·Yuri Kondratiev·Peter Kuchling·Eugene Lytvynov·Maria Joao Oliveira
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Abstract

We study analysis on the cone of discrete Radon measures over a locally compact Polish space $X$. We discuss probability measures on the cone and the corresponding correlation measures and correlation functions on the sub-cone of finite discrete Radon measures over $X$. For this, we consider on the cone an analogue of the harmonic analysis on the configuration space developed in [12]. We also study elements of the difference calculus on the cone: we introduce discrete birth-and-death gradients and study the corresponding Dirichlet forms; finally, we discuss a system of polynomial functions on the cone which satisfy the binomial identity.

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Dmitri Finkelshtein, Yuri Kondratiev, Peter Kuchling, Eugene Lytvynov, Maria Joao Oliveira. 2023-12-06. Analysis on the cone of discrete Radon measures. https://arxiv.org/abs/2312.03537

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