An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
| dc.contributor.author | Gómez-Ullate Otaiza, David | |
| dc.contributor.author | Kamran, Niky | |
| dc.contributor.author | Milson, Robert | |
| dc.date.accessioned | 2023-06-20T03:53:47Z | |
| dc.date.available | 2023-06-20T03:53:47Z | |
| dc.date.issued | 2009-11-01 | |
| dc.description | © 2009 Elsevier Inc. All rights reserved. We are grateful to Jorge Arvesú, Mourad Ismail, Francisco Marcellán and André Ronveaux for their helpful comments. A special note of thanks goes to Norrie Everitt for his suggestions and remarks regarding operator domains and the limit point/circle analysis, and to Lance Littlejohn for comments regarding classical polynomials with negative integer parameters. The research of DGU is supported in part by the Ramón y Cajal program of the Spanish ministry of Science and Technology and by the DGI under grants MTM2006-00478 and MTM2006-14603. The research of NK is supported in part by NSERC grant RGPIN 105490-2004. The research of RM is supported in part by NSERC grant RGPIN-228057-2004. | |
| dc.description.abstract | We present two infinite sequences of polynomial eigenfunctions of a Sturm-Liouville problem. As opposed to the classical orthogonal polynomial systems, these sequences start with a polynomial of degree one. We denote these polynomials as X(1)-Jacobi and X(1)-Laguerre and we prove that they are orthogonal with respect to a positive definite inner product defined over the compact interval [-1, 1] or the half-line [0, infinity), respectively, and they are a basis of the corresponding L(2) Hilbert spaces. Moreover, we prove a converse statement similar to Bochner's theorem for the classical orthogonal polynomial systems: if a self-adjoint second-order operator has a complete set of polynomial eigenfunctions {p(i)}(i=1)(infinity), then it must be either the X(1)-Jacobi or the X(1)-Laguerre Sturm-Liouville problem. A Rodrigues-type formula can be derived for both of the X(1) polynomial sequences. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Spanish ministry of Science and Technology. Ramón y Cajal program | |
| dc.description.sponsorship | DGI | |
| dc.description.sponsorship | NSERC | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/30809 | |
| dc.identifier.doi | 10.1016/j.jmaa.2009.05.052 | |
| dc.identifier.issn | 0022-247X | |
| dc.identifier.officialurl | http://dx.doi.org/10.1016/j.jmaa.2009.05.052 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.relatedurl | http://arxiv.org/abs/0807.3939 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/44632 | |
| dc.issue.number | 1 | |
| dc.journal.title | Journal of mathematical analysis and applications | |
| dc.language.iso | eng | |
| dc.page.final | 369 | |
| dc.page.initial | 352 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | MTM2006-00478 | |
| dc.relation.projectID | TM2006-14603 | |
| dc.relation.projectID | RGPIN 105490-2004 | |
| dc.relation.projectID | RGPIN-228057-2004 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Differential-equation | |
| dc.subject.keyword | Bochner | |
| dc.subject.keyword | Theorem | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | An extended class of orthogonal polynomials defined by a Sturm-Liouville problem | |
| dc.type | journal article | |
| dc.volume.number | 359 | |
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| dspace.entity.type | Publication |
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