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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211864 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862724411312832512 |
|---|---|
| author | Berezin, Sergey Kuijlaars, Arno B.J. Parra, Iván |
| author_facet | Berezin, Sergey Kuijlaars, Arno B.J. Parra, Iván |
| citation_txt | Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials. Sergey Berezin, Arno B.J. Kuijlaars and Iván Parra. SIGMA 19 (2023), 020, 18 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-21T07:04:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211864 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T07:04:37Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Berezin, Sergey Kuijlaars, Arno B.J. Parra, Iván 2026-01-14T09:52:20Z 2023 Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials. Sergey Berezin, Arno B.J. Kuijlaars and Iván Parra. SIGMA 19 (2023), 020, 18 pages 1815-0659 2020 Mathematics Subject Classification: 42C05; 30E25; 41A21 arXiv:2212.06526 https://nasplib.isofts.kiev.ua/handle/123456789/211864 https://doi.org/10.3842/SIGMA.2023.020 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. S.B. is supported by FWO Senior Postdoc Fellowship, project 12K1823N. A.B.J.K. was supported by the long-term structural funding “Methusalem grant of the Flemish Government”, and by FWO Flanders projects EOS 30889451 and G.0910.20. I.P. was supported by FWO Flanders project G.0910.20. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials Article published earlier |
| spellingShingle | Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials Berezin, Sergey Kuijlaars, Arno B.J. Parra, Iván |
| title | Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials |
| title_full | Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials |
| title_fullStr | Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials |
| title_full_unstemmed | Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials |
| title_short | Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials |
| title_sort | planar orthogonal polynomials as type i multiple orthogonal polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211864 |
| work_keys_str_mv | AT berezinsergey planarorthogonalpolynomialsastypeimultipleorthogonalpolynomials AT kuijlaarsarnobj planarorthogonalpolynomialsastypeimultipleorthogonalpolynomials AT parraivan planarorthogonalpolynomialsastypeimultipleorthogonalpolynomials |