Finite difference calculus in the continuum

Authors

  • Dmitri Finkelshtein Department of Mathematics, Swansea University, UK
  • Yuri Kondratiev Department of Mathematics, University of Bielefeld, Germany and Dragomanov Ukrainian State University, Kyiv, Ukraine
  • Eugene Lytvynov Department of Mathematics, Swansea University, UK
  • Maria João Oliveira DCeT, Universidade Aberta, Lisbon and CMAFcIO, University of Lisbon, Portugal

DOI:

https://doi.org/10.3842/umzh.v77i4.8551

Keywords:

falling factorials; spatial combinatorics; configuration spaces; Newton series; Poisson measure; Wick ordering; canonical commutation relations

Abstract

UDC 517.9

We 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.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 77, No. 4, 2025.

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Published

11.06.2025

Issue

Vol. 77 No. 4 (2025)

Section

Research articles

License

Copyright (c) 2025 Dmitri Finkelshtein, Yuri Kondratiev, Eugene Lytvynov, Maria João Oliveira

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Finkelshtein, Dmitri, et al. “Finite Difference Calculus in the Continuum”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 4, June 2025, pp. 291–292, https://doi.org/10.3842/umzh.v77i4.8551.