Finkelshtein, DmitriKondratiev, YuriKuchling, PeterLytvynov, EugeneOliveira, Maria João2025-09-092025-09-092025Finkelshtein, D., Kondratiev, Y., Kuchling, P., Lytvynov, E., Oliveira, M. J., Analysis on the cone of discrete Radon measures. Pure Appl. Funct. Anal. 10 (2) (2025), 307--329.2189-37642189-3756http://hdl.handle.net/10400.2/20213We 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 [Y. G. Kondratiev, T. Kuna, Harmonic analysis on configuration space. I. General theory, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5 (2002), 201–233.]. We also study elements of finite-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.engCone of discrete Radon measurescorrelation measures and correlation functionsharmonic analysisfinite-difference calculusjournal article