Exceptional Legendre Polynomials and Confluent Darboux Transformations
Exceptional orthogonal polynomials are families of orthogonal polynomials that arise as solutions of Sturm-Liouville eigenvalue problems. They generalize the classical families of Hermite, Laguerre, and Jacobi polynomials by allowing for polynomial sequences that miss a finite number of ''...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211172 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Exceptional Legendre Polynomials and Confluent Darboux Transformations. María Ángeles García-Ferrero, David Gómez-Ullate and Robert Milson. SIGMA 17 (2021), 016, 19 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862724928348880896 |
|---|---|
| author | García-Ferrero, María Ángeles Gómez-Ullate, David Milson, Robert |
| author_facet | García-Ferrero, María Ángeles Gómez-Ullate, David Milson, Robert |
| citation_txt | Exceptional Legendre Polynomials and Confluent Darboux Transformations. María Ángeles García-Ferrero, David Gómez-Ullate and Robert Milson. SIGMA 17 (2021), 016, 19 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Exceptional orthogonal polynomials are families of orthogonal polynomials that arise as solutions of Sturm-Liouville eigenvalue problems. They generalize the classical families of Hermite, Laguerre, and Jacobi polynomials by allowing for polynomial sequences that miss a finite number of ''exceptional'' degrees. In this paper, we introduce a new construction of multi-parameter exceptional Legendre polynomials by considering the isospectral deformation of the classical Legendre operator. Using confluent Darboux transformations and a technique from inverse scattering theory, we obtain a fully explicit description of the operators and polynomials in question. The main novelty of the paper is the novel construction that allows for exceptional polynomial families with an arbitrary number of real parameters.
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| first_indexed | 2026-03-21T07:43:27Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211172 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T07:43:27Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | García-Ferrero, María Ángeles Gómez-Ullate, David Milson, Robert 2025-12-25T13:21:37Z 2021 Exceptional Legendre Polynomials and Confluent Darboux Transformations. María Ángeles García-Ferrero, David Gómez-Ullate and Robert Milson. SIGMA 17 (2021), 016, 19 pages 1815-0659 2020 Mathematics Subject Classification: 33C47; 34L10; 34A05 arXiv:2008.02822 https://nasplib.isofts.kiev.ua/handle/123456789/211172 https://doi.org/10.3842/SIGMA.2021.016 Exceptional orthogonal polynomials are families of orthogonal polynomials that arise as solutions of Sturm-Liouville eigenvalue problems. They generalize the classical families of Hermite, Laguerre, and Jacobi polynomials by allowing for polynomial sequences that miss a finite number of ''exceptional'' degrees. In this paper, we introduce a new construction of multi-parameter exceptional Legendre polynomials by considering the isospectral deformation of the classical Legendre operator. Using confluent Darboux transformations and a technique from inverse scattering theory, we obtain a fully explicit description of the operators and polynomials in question. The main novelty of the paper is the novel construction that allows for exceptional polynomial families with an arbitrary number of real parameters. MAGF would like to thank the Max-Planck-Institute for Mathematics in the Sciences, Leipzig (Germany), where some of her work took place. DGU acknowledges support from the Spanish MICINN under grants PGC2018-096504-B-C33 and RTI2018-100754-B-I00 and the European Union under the 2014-2020 ERDF Operational Programme and by the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia (project FEDERUCA18-108393). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Exceptional Legendre Polynomials and Confluent Darboux Transformations Article published earlier |
| spellingShingle | Exceptional Legendre Polynomials and Confluent Darboux Transformations García-Ferrero, María Ángeles Gómez-Ullate, David Milson, Robert |
| title | Exceptional Legendre Polynomials and Confluent Darboux Transformations |
| title_full | Exceptional Legendre Polynomials and Confluent Darboux Transformations |
| title_fullStr | Exceptional Legendre Polynomials and Confluent Darboux Transformations |
| title_full_unstemmed | Exceptional Legendre Polynomials and Confluent Darboux Transformations |
| title_short | Exceptional Legendre Polynomials and Confluent Darboux Transformations |
| title_sort | exceptional legendre polynomials and confluent darboux transformations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211172 |
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