Finite difference calculus in the continuum
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 M...
Saved in:
| Date: | 2026 |
|---|---|
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8551 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: | |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1862224431832629248 |
|---|---|
| author | Finkelshtein, Dmitri Kondratiev, Yuri Lytvynov, Eugene Oliveira, Maria João Finkelshtein, Dmitri Kondratiev, Yuri Lytvynov, Eugene Oliveira, Maria João |
| author_facet | Finkelshtein, Dmitri Kondratiev, Yuri Lytvynov, Eugene Oliveira, Maria João Finkelshtein, Dmitri Kondratiev, Yuri Lytvynov, Eugene Oliveira, Maria João |
| author_sort | Finkelshtein, Dmitri |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-04-11T12:35:37Z |
| description | 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. |
| doi_str_mv | 10.3842/umzh.v77i4.8551 |
| first_indexed | 2026-03-24T03:40:10Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8551 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-04-12T01:00:11Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-85512026-04-11T12:35:37Z Finite difference calculus in the continuum Finite difference calculus in the continuum Finkelshtein, Dmitri Kondratiev, Yuri Lytvynov, Eugene Oliveira, Maria João Finkelshtein, Dmitri Kondratiev, Yuri Lytvynov, Eugene Oliveira, Maria João falling factorials; spatial combinatorics; configuration spaces; Newton series; Poisson measure; Wick ordering; canonical commutation relations 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. УДК 517.9 Скінченнорізницеве числення в континуумі Описано відомі та нові результати скінченнорізницевого числення на конфігураційних просторах. Також наведено скінченнорізницеву геометрію на конфігураційних просторах, пов’язано скінченнорізницеві оператори з канонічними комутаційними співвідношеннями, знайдено явну форму певних скінченнорізницевих марковських генераторів на конфігураційних просторах та описано простори рядів Ньютона, визначених на конфігураційних просторах. Institute of Mathematics, NAS of Ukraine 2026-04-10 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8551 10.3842/umzh.v77i4.8551 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 4 (2025); 291–292 Український математичний журнал; Том 77 № 4 (2025); 291–292 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8551/10448 Copyright (c) 2025 Dmitri Finkelshtein, Yuri Kondratiev, Eugene Lytvynov, Maria João Oliveira |
| spellingShingle | Finkelshtein, Dmitri Kondratiev, Yuri Lytvynov, Eugene Oliveira, Maria João Finkelshtein, Dmitri Kondratiev, Yuri Lytvynov, Eugene Oliveira, Maria João Finite difference calculus in the continuum |
| title | Finite difference calculus in the continuum |
| title_alt | 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_short | Finite difference calculus in the continuum |
| title_sort | finite difference calculus in the continuum |
| topic_facet | falling factorials spatial combinatorics configuration spaces Newton series Poisson measure Wick ordering canonical commutation relations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8551 |
| work_keys_str_mv | AT finkelshteindmitri finitedifferencecalculusinthecontinuum AT kondratievyuri finitedifferencecalculusinthecontinuum AT lytvynoveugene finitedifferencecalculusinthecontinuum AT oliveiramariajoao finitedifferencecalculusinthecontinuum AT finkelshteindmitri finitedifferencecalculusinthecontinuum AT kondratievyuri finitedifferencecalculusinthecontinuum AT lytvynoveugene finitedifferencecalculusinthecontinuum AT oliveiramariajoao finitedifferencecalculusinthecontinuum |