Exceptional Legendre Polynomials and Confluent Darboux Transformations
| Autor: | María Ángeles García-Ferrero, Robert Milson, David Gómez-Ullate |
|---|---|
| Přispěvatelé: | Ingeniería Informática |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Física-Modelos matemáticos
010102 general mathematics FOS: Physical sciences exceptional orthogonal polynomials isospectral deformations Mathematical Physics (math-ph) 010103 numerical & computational mathematics Public administration 01 natural sciences Government (linguistics) Darboux transformations Work (electrical) Mathematics - Classical Analysis and ODEs Classical Analysis and ODEs (math.CA) FOS: Mathematics Física matemática media_common.cataloged_instance Geometry and Topology 0101 mathematics European union Legendre polynomials Analysis Mathematical Physics 33C47 34L10 34A05 media_common |
| Zdroj: | E-Prints Complutense: Archivo Institucional de la UCM Universidad Complutense de Madrid SIGMA 17 (2021), 016, 19 pag RODIN: Repositorio de Objetos de Docencia e Investigación de la Universidad de Cádiz Universidad de Cádiz RODIN. Repositorio de Objetos de Docencia e Investigación de la Universidad de Cádiz instname E-Prints Complutense. Archivo Institucional de la UCM |
| Popis: | 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 FEDER-UCA18-108393). |
| Databáze: | OpenAIRE |
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