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Orthogonal polynomials and Mobius transformations

dc.contributor.authorVieira, R. S.
dc.contributor.authorBotta, V [UNESP]
dc.contributor.institutionUniversidade Federal de São Carlos (UFSCar)
dc.contributor.institutionUniversidade Estadual Paulista (UNESP)
dc.date.accessioned2022-04-28T17:22:01Z
dc.date.available2022-04-28T17:22:01Z
dc.date.issued2021-09-01
dc.description.abstractGiven an orthogonal polynomial sequence on the real line, another sequence of polynomials can be found by composing them with a Mobius transformation. In this work, we study the properties of such Mobius-transformed polynomials in a systematically way. We show that these polynomials are orthogonal on a given curve of the complex plane with respect to a particular kind of varying measure, and that they enjoy several properties common to the orthogonal polynomials on the real line. Moreover, many properties of the orthogonal polynomials can be easier derived from this approach, for example, we can show that the Hermite, Laguerre, Jacobi, Bessel and Romanovski polynomials are all related with each other by suitable Mobius transformations; also, the orthogonality relations for Bessel and Romanovski polynomials on the complex plane easily follows.en
dc.description.affiliationUniv Fed Sao Carlos UFSCar, Dept Matemat, BR-13565905 Sao Carlos, SP, Brazil
dc.description.affiliationUniv Estadual Paulista, Fac Ciencias & Tecnol, Dept Matemat & Comp, UNESP, BR-19060900 Presidente Prudente, SP, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, Fac Ciencias & Tecnol, Dept Matemat & Comp, UNESP, BR-19060900 Presidente Prudente, SP, Brazil
dc.description.sponsorshipCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipIdCAPES: 001
dc.description.sponsorshipIdFAPESP: 2016/02700-8
dc.format.extent27
dc.identifierhttp://dx.doi.org/10.1007/s40314-021-01516-4
dc.identifier.citationComputational & Applied Mathematics. Heidelberg: Springer Heidelberg, v. 40, n. 6, 27 p., 2021.
dc.identifier.doi10.1007/s40314-021-01516-4
dc.identifier.issn2238-3603
dc.identifier.urihttp://hdl.handle.net/11449/218621
dc.identifier.wosWOS:000669311200001
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofComputational & Applied Mathematics
dc.sourceWeb of Science
dc.subjectOrthogonal polynomials
dc.subjectMobius transformations
dc.subjectVarying weight functions
dc.subjectClassical orthogonal polynomials
dc.subjectBessel polynomials
dc.subjectRomanovski polynomials
dc.titleOrthogonal polynomials and Mobius transformationsen
dc.typeArtigo
dcterms.licensehttp://www.springer.com/open+access/authors+rights?SGWID=0-176704-12-683201-0
dcterms.rightsHolderSpringer
dspace.entity.typePublication
unesp.departmentMatemática e Computação - FCTpt

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