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Multidimensional Toda Lattices: Continuous and Discrete Time
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Multidimensional Toda Lattices: Continuous and Discrete Time
Інший ID:
2010 Mathematics Subject Classification: 42C05; 37K10; 39A14; 65Q10
DOI:10.3842/SIGMA.2016.054
DOI:10.3842/SIGMA.2016.054
Посилання:
Multidimensional Toda Lattices: Continuous and Discrete Time / A.I. Aptekarev, M. Derevyagin, H. Miki, W. Van Assche // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 56 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications.
The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html.
A.I. Aptekarev was supported by grant RScF-14-21-00025. M. Derevyagin thanks the hospitality
of Department of Mathematics of KU Leuven, where his part of the research was initiated while
he was a postdoc there. M. Derevyagin and W. Van Assche gratefully acknowledge the support
of FWO Flanders project G.0934.13, KU Leuven research grant OT/12/073 and the Belgian
Interuniversity Attraction Poles programme P07/18. H. Miki was supported by JSPS KAKENHI
Grant Number 15K17561. Also, M. Derevyagin and H. Miki are grateful to S. Tsujimoto,
L. Vinet, A. Zhedanov for valuable discussions and comments. Finally, all the authors thank
the anonymous referees for their careful reading of the manuscript and for their remarks that
improved the presentation of the paper.
Дата:
2016
Переглядів:
560
Завантажень:
273
Анотація:
In this paper we present multidimensional analogues of both the continuous- and discrete-time Toda lattices. The integrable systems that we consider here have two or more space coordinates. To construct the systems, we generalize the orthogonal polynomial approach for the continuous and discrete Toda lattices to the case of multiple orthogonal polynomials.
