dc.creator | Álvarez Nodarse, Renato | es |
dc.creator | Soares Petronilho, José Carlos | es |
dc.creator | Pinzón Cortés, Natalia Camila | es |
dc.creator | Sevinik Adigüzel, Rezan | es |
dc.date.accessioned | 2016-06-01T10:07:43Z | |
dc.date.available | 2016-06-01T10:07:43Z | |
dc.date.issued | 2015-08-15 | |
dc.identifier.citation | Álvarez Nodarse, R., Soares Petronilho, J.C., Pinzón Cortés, N.C. y Sevinik Adigüzel, R. (2015). On linearly related sequences of difference derivatives of discrete orthogonal polynomials. Journal of Computational and Applied Mathematics, 284, 26-37. | |
dc.identifier.issn | 0377-0427 | es |
dc.identifier.uri | http://hdl.handle.net/11441/41765 | |
dc.description.abstract | Let ν be either ω ∈ C \ {0} or q ∈ C \ {0, 1}, and let Dν be the corresponding difference operator defined in the usual way either by Dωp(x) = p(x+ω)−p(x)
ω or Dqp(x) = p(qx)−p(x) (q−1)x. Let U and V be two moment regular linear functionals and let {Pn(x)}n≥0 and {Qn(x)}n≥0 be their corresponding orthogonal polynomial sequences (OPS). We discuss an inverse problem
in the theory of discrete orthogonal polynomials involving the two OPS {Pn(x)}n≥0 and {Qn(x)}n≥0 assuming that their difference derivatives Dν of higher orders m and k (resp.) are connected by a linear algebraic structure relation such as X M i=0 ai,nDm ν Pn+m−i(x) = X N i=0 bi,nDk νQn+k−i(x), n ≥ 0, where M, N, m, k ∈ N ∪ {0}, aM,n 6= 0 for n ≥ M, bN,n 6= 0 for n ≥ N, and ai,n = bi,n = 0 for i > n. Under certain conditions, we prove that U and V are related by a rational factor (in the ν−distributional sense). Moreover, when m 6= k then both U and V are Dν-semiclassical functionals. This leads us to the concept of (M, N)-Dν-coherent pair of order (m, k) extending to the discrete case several previous works. As an application we consider the OPS with respect to the following Sobolev-type inner product hp(x), r(x)iλ,ν = hU, p(x)r(x)i + λ hV,(Dm ν p)(x)(Dm ν r)(x)i, λ > 0, assuming that U and V (which, eventually, may be represented by discrete measures supported either on a uniform lattice if ν = ω, or on a q-lattice if ν = q) constitute a (M, N)-Dν-coherent pair of order m (that is, an (M, N)-Dν-coherent pair of order (m, 0)), m ∈ N being fixed. | es |
dc.description.sponsorship | Ministerio de Economía y Competitividad | es |
dc.description.sponsorship | Junta de Andalucía | es |
dc.description.sponsorship | Fondo Europeo de Desarrollo Regional | es |
dc.description.sponsorship | Fundaçao para a Ciência e a Tecnologia (Portugal) | es |
dc.description.sponsorship | Scientific and Technological Research Council of Turkey | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Elsevier | es |
dc.relation.ispartof | Journal of Computational and Applied Mathematics, 284, 26-37. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Orthogonal polynomials | es |
dc.subject | inverse problems | es |
dc.subject | semiclassical orthogonal polynomials | es |
dc.subject | coherent pairs | es |
dc.subject | Sobolev-type orthogonal polynomials | es |
dc.title | On linearly related sequences of difference derivatives of discrete orthogonal polynomials | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Análisis Matemático | es |
dc.relation.projectID | info:eu-repo/grantAgreement/MINECO/MTM2012-36732-C03 | es |
dc.relation.projectID | FQM-262 | es |
dc.relation.projectID | FQM-7276 | es |
dc.relation.projectID | P09-FQM-4643 | es |
dc.relation.projectID | PEst-C/MAT/UI0324/2013 | es |
dc.relation.publisherversion | http://dx.doi.org/10.1016/j.cam.2014.06.018 | |
dc.identifier.doi | 10.1016/j.cam.2014.06.018 | es |
idus.format.extent | 20 p. | es |
dc.journaltitle | Journal of Computational and Applied Mathematics | es |
dc.publication.volumen | 284 | es |
dc.publication.initialPage | 26 | es |
dc.publication.endPage | 37 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/41765 | |