Theory of classical orthogonal polynomials in terms of discrete integrable systems and its applications

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400110
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyoto University
• Principal Investigator: TSUJIMOTO SATOSHI 京都大学, 情報学研究科, 准教授 (60287977)
• Co-Investigator(Kenkyū-buntansha): Nakamura Yoshimasa 京都大学, 大学院情報学研究科, 教授 (50172458)
• Co-Investigator(Renkei-kenkyūsha): Kato Tsuyoshi 京都大学, 大学院理学研究科, 教授 (20273427)
• Project Period (FY): 2013-04-01 – 2016-03-31
• 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

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.

Free Research Field

直交多項式、離散可積分系