Finite Difference Calculus in the Continuum

Finkelshtein, Dmitri; Kondratiev, Yuri; Lytvynov, Eugene; Oliveira, Maria João

doi:10.1007/s11253-025-02482-4

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Finite Difference Calculus in the Continuum

Dmitri Finkelshtein

, Yuri Kondratiev, Eugene Lytvynov

, Maria João Oliveira

Ukrainian Mathematical Journal, Volume: 77, Issue: 4, Pages: 679 - 698

Swansea University Authors: Dmitri Finkelshtein , Eugene Lytvynov

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DOI (Published version): 10.1007/s11253-025-02482-4

Abstract

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 gene...

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Published in:	Ukrainian Mathematical Journal
ISSN:	0041-5995 1573-9376
Published:	Springer Nature 2025
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa68123

first_indexed	2024-10-31T11:42:47Z
last_indexed	2025-10-24T17:59:43Z
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spelling	2025-10-23T13:27:19.0290089 v2 68123 2024-10-31 Finite Difference Calculus in the Continuum 4dc251ebcd7a89a15b71c846cd0ddaaf 0000-0001-7136-9399 Dmitri Finkelshtein Dmitri Finkelshtein true false e5b4fef159d90a480b1961cef89a17b7 0000-0001-9685-7727 Eugene Lytvynov Eugene Lytvynov true false 2024-10-31 MACS 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. Journal Article Ukrainian Mathematical Journal 77 4 679 698 Springer Nature 0041-5995 1573-9376 30 9 2025 2025-09-30 10.1007/s11253-025-02482-4 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University SU Library paid the OA fee (TA Institutional Deal) MJO was supported by the Portuguese national funds through FCT–Fundação para a Ciência e a Tecnologia, within the project UIDB/04561/2020 (https://doi.org/10.54499/UIDB/04561/2020). 2025-10-23T13:27:19.0290089 2024-10-31T11:37:26.9492355 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Dmitri Finkelshtein 0000-0001-7136-9399 1 Yuri Kondratiev 2 Eugene Lytvynov 0000-0001-9685-7727 3 Maria João Oliveira 4 68123__35451__10d16e5379fa434bbb03624ad5cc851f.pdf 68123.VOR.pdf 2025-10-23T13:14:23.9342049 Output 180806 application/pdf Version of Record true © The Author(s) 2025. This article is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). true eng http://creativecommons.org/licenses/by/4.0/
title	Finite Difference Calculus in the Continuum
spellingShingle	Finite Difference Calculus in the Continuum Dmitri Finkelshtein Eugene Lytvynov
title_short	Finite Difference Calculus in the Continuum
title_full	Finite Difference Calculus in the Continuum
title_fullStr	Finite Difference Calculus in the Continuum
title_full_unstemmed	Finite Difference Calculus in the Continuum
title_sort	Finite Difference Calculus in the Continuum
author_id_str_mv	4dc251ebcd7a89a15b71c846cd0ddaaf e5b4fef159d90a480b1961cef89a17b7
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author	Dmitri Finkelshtein Eugene Lytvynov
author2	Dmitri Finkelshtein Yuri Kondratiev Eugene Lytvynov Maria João Oliveira
format	Journal article
container_title	Ukrainian Mathematical Journal
container_volume	77
container_issue	4
container_start_page	679
publishDate	2025
institution	Swansea University
issn	0041-5995 1573-9376
doi_str_mv	10.1007/s11253-025-02482-4
publisher	Springer Nature
college_str	Faculty of Science and Engineering
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hierarchy_top_title	Faculty of Science and Engineering
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department_str	School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
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description	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.
published_date	2025-09-30T05:23:27Z
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Finite Difference Calculus in the Continuum

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