On q-Deformations of the Heun Equation
The q-Heun equation and its variants arise as degenerations of Ruijsenaars-van Diejen operators with one particle. We investigate local properties of these equations. In particular, we characterize the variants of the q-Heun equation by using analysis of regular singularities. We also consider the q...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2018 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209789 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On q-Deformations of the Heun Equation / K. Takemura // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 12 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862547205478416384 |
|---|---|
| author | Takemura, K. |
| author_facet | Takemura, K. |
| citation_txt | On q-Deformations of the Heun Equation / K. Takemura // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The q-Heun equation and its variants arise as degenerations of Ruijsenaars-van Diejen operators with one particle. We investigate local properties of these equations. In particular, we characterize the variants of the q-Heun equation by using analysis of regular singularities. We also consider the quasi-exact solvability of the q-Heun equation and its variants. Namely, we investigate finite-dimensional subspaces that are invariant under the action of the q-Heun operator or variants of the q-Heun operator.
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| first_indexed | 2025-12-03T19:58:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209789 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-03T19:58:07Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Takemura, K. 2025-11-26T12:24:29Z 2018 On q-Deformations of the Heun Equation / K. Takemura // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 12 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 39A13; 33E10 arXiv: 1712.09564 https://nasplib.isofts.kiev.ua/handle/123456789/209789 https://doi.org/10.3842/SIGMA.2018.061 The q-Heun equation and its variants arise as degenerations of Ruijsenaars-van Diejen operators with one particle. We investigate local properties of these equations. In particular, we characterize the variants of the q-Heun equation by using analysis of regular singularities. We also consider the quasi-exact solvability of the q-Heun equation and its variants. Namely, we investigate finite-dimensional subspaces that are invariant under the action of the q-Heun operator or variants of the q-Heun operator. The author is grateful to Simon Ruijsenaars for valuable comments and fruitful discussions. He thanks the referees and the editor for their useful comments. He is supported by JSPS KAKENHI Grant Number JP26400122. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On q-Deformations of the Heun Equation Article published earlier |
| spellingShingle | On q-Deformations of the Heun Equation Takemura, K. |
| title | On q-Deformations of the Heun Equation |
| title_full | On q-Deformations of the Heun Equation |
| title_fullStr | On q-Deformations of the Heun Equation |
| title_full_unstemmed | On q-Deformations of the Heun Equation |
| title_short | On q-Deformations of the Heun Equation |
| title_sort | on q-deformations of the heun equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209789 |
| work_keys_str_mv | AT takemurak onqdeformationsoftheheunequation |