A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type
We present a representation of skew-orthogonal polynomials of symplectic type ( = 4) in terms of a matrix Riemann-Hilbert problem, for weights of the form e⁻ⱽ⁽ᶻ⁾ where is a polynomial of even degree and positive leading coefficient. This is done by representing skew-orthogonality as a kind of multi...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212344 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type. Alex Little. SIGMA 20 (2024), 076, 32 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We present a representation of skew-orthogonal polynomials of symplectic type ( = 4) in terms of a matrix Riemann-Hilbert problem, for weights of the form e⁻ⱽ⁽ᶻ⁾ where is a polynomial of even degree and positive leading coefficient. This is done by representing skew-orthogonality as a kind of multiple-orthogonality. From this, we derive a = 4 analogue of the Christoffel-Darboux formula. Finally, our Riemann-Hilbert representation allows us to derive a Lax pair whose compatibility condition may be viewed as a = 4 analogue of the Toda lattice.
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| ISSN: | 1815-0659 |