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Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8, випуск за цей рік
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Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems
Інший ID:
2010 Mathematics Subject Classification: 42C05; 35C05; 37K60; 15B52
DOI: http://dx.doi.org/10.3842/SIGMA.2012.008
DOI: http://dx.doi.org/10.3842/SIGMA.2012.008
Посилання:
Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems / H. Miki, H. Goda, S. Tsujimoto // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 27 назв. — англ.
Підтримка:
The authors would like to thank the Centre de recherches math´ematiques (CRM) for its hospitality. The work of H.M. is partially supported by a Grant-in-Aid for Japan Society for the
Promotion of Science (JSPS) Fellows. The research of S.T. is supported in part by KAKENHI (22540224). The authors should like to thank the referees for the careful reading of the
manuscript and a lot of helpful suggestions and comments.
Дата:
2012
Переглядів:
666
Завантажень:
383
Анотація:
Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the (2+1)-dimensional case, the corresponding system can be extended to 2×2 matrix form. The factorization theorem of the Christoffel kernel for skew orthogonal polynomials in random matrix theory is presented as a by-product of these transformations.
