Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials
A recent result of S.-Y. Lee and M. Yang state that the planar orthogonal polynomials orthogonal with respect to a modified Gaussian measure are multiple orthogonal polynomials of type II on a contour in the complex plane. We show that the same polynomials are also type I orthogonal polynomials on a...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2023 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2023
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211864 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials. Sergey Berezin, Arno B.J. Kuijlaars and Iván Parra. SIGMA 19 (2023), 020, 18 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | A recent result of S.-Y. Lee and M. Yang state that the planar orthogonal polynomials orthogonal with respect to a modified Gaussian measure are multiple orthogonal polynomials of type II on a contour in the complex plane. We show that the same polynomials are also type I orthogonal polynomials on a contour, provided the exponents in the weight are integers. From this orthogonality, we derive several equivalent Riemann-Hilbert problems. The proof is based on the fundamental identity of Lee and Yang, which we establish using a new technique.
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| ISSN: | 1815-0659 |