Finkelshtein, DmitriKondratiev, YuriLytvynov, EugeneOliveira, Maria João2025-10-232025-10-232025-10-22Finkelshtein, D., Kondratiev, Y., Lytvynov, E. et al. Finite Difference Calculus in the Continuum. Ukr Math J (2025). https://doi.org/10.1007/s11253-025-02482-4http://hdl.handle.net/10400.2/20387We describe known and new results on the finite-difference calculus on configuration spaces. We also describe the finite-difference geometry on configuration spaces, relate finite-difference operators to the canonical commutation relations, find explicit form of certain finite-difference Markov generators on configuration spaces, and describe spaces of Newton series defined over the configuration spaces.engFalling factorialsPatial combinatoricsConfiguration spacesNewton seriesPoisson measureWick orderingCanonical commutation relationsjournal article10.1007/s11253-025-02482-4