When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?

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dc.creatorAlfaro, M.
dc.creatorMarcellan, F.
dc.creatorPena, A.
dc.creatorRezola, M. L.
dc.date2007-11-12
dc.date.accessioned2026-07-07T08:42:20Z
dc.date.available2026-07-07T08:42:20Z
dc.descriptionGiven $\{P_n \}$ a sequence of monic orthogonal polynomials, we analyze their linear combinations $\{Q_n \}$with constant coefficients and fixed length $k+1$. Necessary and sufficient conditions are given for the orthogonality of the monic sequence $\{Q_n \}$ as well as an interesting interpretation in terms of the Jacobi matrices associated with $\{P_n \}$ and $\{Q_n \}$. Moreover, in the case $k=2$, we characterize the families $\{P_n \}$ such that the corresponding polynomials $\{Q_n \}$ are also orthogonal.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/0711.1740
dc.identifierhttp://arxiv.org/abs/0711.1740
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141925
dc.subjectClassical Analysis and ODEs
dc.subject33C45, 42C05
dc.titleWhen do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?
dc.typetext

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