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On linearly related sequences of difference derivatives of discrete orthogonal polynomials

 

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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
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
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