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Characterization of orthogonal polynomials on lattices
dc.contributor.author | Mbouna, Dieudonné | |
dc.contributor.author | Mañas Mañas, Juan Francisco | |
dc.contributor.author | Moreno Balcázar, Juan José | |
dc.date.accessioned | 2024-03-15T08:15:44Z | |
dc.date.available | 2024-03-15T08:15:44Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | D. Mbouna, Juan F. Mañas–Mañas & Juan J. Moreno–Balcázar (2023) Characterization of orthogonal polynomials on lattices, Integral Transforms and Special Functions, 34 (9), 675-689, DOI: 10.1080/10652469.2023.2182775 | es_ES |
dc.identifier.issn | 1065-2469 | |
dc.identifier.uri | http://hdl.handle.net/10835/16161 | |
dc.description.abstract | We consider two sequences of orthogonal polynomials $(P_n)_{n\geq 0}$ and $(Q_n)_{n\geq 0}$ such that \begin{align*} \sum_{j=1} ^{M} a_{j,n}\mathrm{S}_x\mathrm{D}_x ^k P_{k+n-j} (z)=\sum_{j=1} ^{N} b_{j,n}\mathrm{D}_x ^{m} Q_{m+n-j} (z)\;, \end{align*} with $k,m,M,N \in \mathbb{N}$, $a_{j,n}$ and $b_{j,n}$ are sequences of complex numbers, $$2\mathrm{S}_xf(x(s))=(\triangle +2\mathrm{I})f(z),\quad \mathrm{D}_xf(x(s))=\frac{\triangle}{\triangle x(s-1/2)}f(z),$$ $z=x(s-1/2)$, $\mathrm{I}$ is the identity operator, $x$ defines a lattice, and $\triangle f(s)=f(s+1)-f(s)$. We show that under some natural conditions, both involved orthogonal polynomials sequences $(P_n)_{n\geq 0}$ and $(Q_n)_{n\geq 0}$ are semiclassical whenever $k=m$. Some particular cases are studied closely where we characterize the continuous dual Hahn and Wilson polynomials for quadratic lattices. | es_ES |
dc.language.iso | en | es_ES |
dc.publisher | https://www.tandfonline.com/doi/full/10.1080/10652469.2023.2182775 | es_ES |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Mathematics | es_ES |
dc.subject | Semiclassical functional | es_ES |
dc.subject | Wilson polynomials | es_ES |
dc.subject | continuous dual Hahn polynomials | es_ES |
dc.subject | lattices | es_ES |
dc.title | Characterization of orthogonal polynomials on lattices | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.relation.publisherversion | https://doi.org/10.1080/10652469.2023.2182775 | es_ES |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es_ES |
dc.relation.projectID | Grant number UAL18-FQM-B025-A, Grant number PID2021-124472NB-I00. | es_ES |