RT Journal Article
T1 A conjecture on exceptional orthogonal polynomials
A1 Gómez-Ullate Otaiza, David
A1 Kamran, Niky
A1 Milson, Robert
AB Exceptional orthogonal polynomial systems (X-OPSs) arise as eigenfunctions of Sturm-Liouville problems, but without the assumption that an eigenpolynomial of every degree is present. In this sense, they generalize the classical families of Hermite, Laguerre, and Jacobi, and include as a special case the family of CPRS orthogonal polynomials introduced by Cariena et al. (J. Phys. A 41:085301, 2008). We formulate the following conjecture: every exceptional orthogonal polynomial system is related to a classical system by a Darboux-Crum transformation. We give a proof of this conjecture for codimension 2 exceptional orthogonal polynomials (X-2-OPs). As a by-product of this analysis, we prove a Bochner-type theorem classifying all possible X-2-OPSs. The classification includes all cases known to date plus some new examples of X-2-Laguerre and X-2-Jacobi polynomials.
PB Springer
SN 1615-3375
YR 2013
FD 2013-08
LK https://hdl.handle.net/20.500.14352/34711
UL https://hdl.handle.net/20.500.14352/34711
LA eng
NO © Springer. The research of DGU was supported in part by MICINN-FEDER grant MTM2009- 06973 and CUR-DIUE grant 2009SGR859. The research of NK was supported in part by NSERC grant RGPIN 105490-2011. The research of RM was supported in part by NSERC grant RGPIN-228057-2009.
NO MICINN-FEDER
NO CUR-DIUE
NO NSERC
DS Docta Complutense
RD 6 abr 2025