RT journal article
T1 Exceptional Legendre Polynomials and Confluent Darboux Transformations
A1 García-Ferrero, María Ángeles
A1 Gómez-Ullate Oteiza, David
A1 Milson, Robert
A2 Ingeniería Informática
K1 exceptional orthogonal polynomials
K1 Darboux transformations
K1 isospectral deformations
AB 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.
PB NATL ACAD SCI UKRAINE
SN 1815-0659
YR 2021
FD 2021
LK http://hdl.handle.net/10498/24755
UL http://hdl.handle.net/10498/24755
LA eng
NO 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).
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026