Publication:
On linearly related sequences of difference derivatives of discrete orthogonal polynomials

Simple item page
dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorÁlvarez-Nodarse, Renato
dc.contributor.authorPetronilho, José
dc.contributor.authorPinzón-Cortés, Natalia Camila
dc.contributor.authorSevinik-Adıgüzel, Rezan
dc.date.accessioned2016-07-21T08:42:40Z
dc.date.available2017-08-15T22:00:07Z
dc.date.issued2015-08-15
dc.descriptionProceedings of: OrthoQuad 2014. Puerto de la Cruz, Tenerife, Spain. January 20–24, 2014en
dc.description.abstractLet 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 ∑Mi=0ai,nDmνPn+m−i(x)=∑Ni=0bi,nDkνQn+k−i(x),n≥0, Turn MathJax off where M,N,m,k∈N∪{0} , aM,n≠0 for n≥M , bN,n≠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≠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 ⟨p(x),r(x)⟩λ,ν=⟨U,p(x)r(x)⟩+λ⟨V,(Dmνp)(x)(Dmνr)(x)⟩,λ>0, Turn MathJax off 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.en
dc.description.sponsorshipWe are grateful to Prof. Francisco Marcellán for his valuable comments and remarks that helped us to improve the paper. This work was supported by Dirección General de Investigación, Desarrollo e Innovación, Ministerio de Economía y Competitividad of Spain, under grants MTM2012-36732-C03 (RAN, NCP-C, JP), Junta de Andalucía (Spain) under grants FQM262, FQM-7276, and P09-FQM-4643 (RAN), FEDER funds (RAN)en
dc.format.extent12
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationJournal of Computational and Applied Mathematics, 2015, v. 284, pp. 26–37en
dc.identifier.doi10.1016/j.cam.2014.06.018
dc.identifier.issn0377-0427
dc.identifier.publicationfirstpage26
dc.identifier.publicationlastpage37
dc.identifier.publicationtitleJournal of Computational and Applied Mathematicsen
dc.identifier.publicationvolume284
dc.identifier.urihttps://hdl.handle.net/10016/23405
dc.language.isoengen
dc.publisherElsevier
dc.relation.eventdateJanuary 20–24, 2014en
dc.relation.eventplacePuerto de la Cruz, Tenerife, Spaines
dc.relation.eventtitleOrthoQuad 2014
dc.relation.projectIDGobierno de España. MTM-2012-36732-C03-01es
dc.relation.publisherversionhttp://dx.doi.org/10.1016/j.cam.2014.06.018
dc.rights© Elsevier 2015
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen access
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherOrthogonal polynomialsen
dc.subject.otherInverse problemsen
dc.subject.otherSemiclassical orthogonal polynomialsen
dc.subject.otherCoherent pairsen
dc.subject.otherSobolev-type orthogonal polynomialsen
dc.titleOn linearly related sequences of difference derivatives of discrete orthogonal polynomialsen
dc.typeconference paper*
dc.type.hasVersionAM*
dspace.entity.typePublication
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
linearly_alvarez_JCAM_2015_ps.pdf
Size:
668.23 KB
Format:
Adobe Portable Document Format
Description:
Download
Collections
DM - GAMA - Artículos de Revistas
DM - GAMA - Comunicaciones en Congresos y otros eventos