Theory of classical orthogonal polynomials in terms of discrete integrable systems and its applications
| Project/Area Number |
25400110
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
Nakamura Yoshimasa 京都大学, 大学院情報学研究科, 教授 (50172458)
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| Co-Investigator(Renkei-kenkyūsha) |
Kato Tsuyoshi 京都大学, 大学院理学研究科, 教授 (20273427)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 力学系・可積分系 / 直交多項式 / 特殊関数 / 古典直交多項式 / 例外型直交多項式 / 箱玉系 / オートマトン / 離散可積分系 / 国際研究者交流 ウクライナ |
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| Outline of Final Research Achievements |
By using the theory of integrable systems, we study the classical orthogonal functions. In this study, we have succeeded in deriving the recurrence relations for the exceptional orthogonal polynomials as a generalization of the classical orthogonal polynomials. The Bannai-Ito algebra is also presented together with some of its applications. In its relations with the Bannai-Ito polynomials, an exceptional orthogonal polynomial analogue is introduced by using the generalized Darboux transformations. We also formulate integrable ultradiscrete systems like box-ball system in the language of automata, and then study using the methods standard in automata theory.
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Report
(4 results)
Research Products
(12 results)
