Basic Properties of Non-Stationary Ruijsenaars Functions
For any variable number, a non-stationary Ruijsenaars function was recently introduced as a natural generalization of an explicitly known asymptotically free solution of the trigonometric Ruijsenaars model, and it was conjectured that this non-stationary Ruijsenaars function provides an explicit sol...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211015 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Basic Properties of Non-Stationary Ruijsenaars Functions. Edwin Langmann, Masatoshi Noumi and Junichi Shiraishi. SIGMA 16 (2020), 105, 26 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860054873103400960 |
|---|---|
| author | Langmann, Edwin Noumi, Masatoshi Shiraishi, Junichi |
| author_facet | Langmann, Edwin Noumi, Masatoshi Shiraishi, Junichi |
| citation_txt | Basic Properties of Non-Stationary Ruijsenaars Functions. Edwin Langmann, Masatoshi Noumi and Junichi Shiraishi. SIGMA 16 (2020), 105, 26 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For any variable number, a non-stationary Ruijsenaars function was recently introduced as a natural generalization of an explicitly known asymptotically free solution of the trigonometric Ruijsenaars model, and it was conjectured that this non-stationary Ruijsenaars function provides an explicit solution of the elliptic Ruijsenaars model. We present alternative series representations of the non-stationary Ruijsenaars functions, and we prove that these series converge. We also introduce novel difference operators called , which, as we prove in the trigonometric limit and conjecture in the general case, act diagonally on the non-stationary Ruijsenaars functions.
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| first_indexed | 2026-03-19T02:15:59Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211015 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T02:15:59Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Langmann, Edwin Noumi, Masatoshi Shiraishi, Junichi 2025-12-22T09:28:54Z 2020 Basic Properties of Non-Stationary Ruijsenaars Functions. Edwin Langmann, Masatoshi Noumi and Junichi Shiraishi. SIGMA 16 (2020), 105, 26 pages 1815-0659 2020 Mathematics Subject Classification: 81Q80; 32A17; 33E20; 33E30 arXiv:2006.07171 https://nasplib.isofts.kiev.ua/handle/123456789/211015 https://doi.org/10.3842/SIGMA.2020.105 For any variable number, a non-stationary Ruijsenaars function was recently introduced as a natural generalization of an explicitly known asymptotically free solution of the trigonometric Ruijsenaars model, and it was conjectured that this non-stationary Ruijsenaars function provides an explicit solution of the elliptic Ruijsenaars model. We present alternative series representations of the non-stationary Ruijsenaars functions, and we prove that these series converge. We also introduce novel difference operators called , which, as we prove in the trigonometric limit and conjecture in the general case, act diagonally on the non-stationary Ruijsenaars functions. We would like to thank F. Atai, A. Negut, andV. Pasquier for useful discussions. We thank J. Lamers for a helpful comment on the manuscript. We are grateful to the careful referees for their remarks, helping us to improve our paper. This work is supported by VR Grant No 2016-05167 (E.L.) and by JSPS Kakenhi Grants (B)15H03626 (M.N.), (C) 19K03512 (J.S.). MN gratefully acknowledges financial support from the Knut and Alice Wallenberg Foundation (KAW 2019.0525). We are grateful to the Stiftelse Olle Engkvist Byggmastare, Contract 184-0573, for financial support. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Basic Properties of Non-Stationary Ruijsenaars Functions Article published earlier |
| spellingShingle | Basic Properties of Non-Stationary Ruijsenaars Functions Langmann, Edwin Noumi, Masatoshi Shiraishi, Junichi |
| title | Basic Properties of Non-Stationary Ruijsenaars Functions |
| title_full | Basic Properties of Non-Stationary Ruijsenaars Functions |
| title_fullStr | Basic Properties of Non-Stationary Ruijsenaars Functions |
| title_full_unstemmed | Basic Properties of Non-Stationary Ruijsenaars Functions |
| title_short | Basic Properties of Non-Stationary Ruijsenaars Functions |
| title_sort | basic properties of non-stationary ruijsenaars functions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211015 |
| work_keys_str_mv | AT langmannedwin basicpropertiesofnonstationaryruijsenaarsfunctions AT noumimasatoshi basicpropertiesofnonstationaryruijsenaarsfunctions AT shiraishijunichi basicpropertiesofnonstationaryruijsenaarsfunctions |