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arXiv · 1910.03039

On the Darboux transformations and sequences of $p$-orthogonal polynomials

D. Barrios Rolanía·J. C. García-Ardila·D. Manrique
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Abstract

For a fixed $p \in \mathbb{N}$, sequences of polynomials $\{P_n\}$, $n \in \mathbb{N}$, defined by a $(p+2)$-term recurrence relation are related to several topics in Approximation Theory. A $(p+2)$-banded matrix $J$ determines the coefficients of the recurrence relation of any of such sequences of polynomials. The connection between these polynomials and the concept of orthogonality has been already established through a $p$-dimension vector of functionals. This work goes further in this topic by analyzing the relation between such vectors for the set of sequences $\{P_n^{(j)}\}$, $n \in N$, associated with the Darboux transformations $J^{(j)}$, $j=1, ..., p,$ of a given $(p+2)$-banded matrix $J$.

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D. Barrios Rolanía, J. C. García-Ardila, D. Manrique. 2019-10-07. On the Darboux transformations and sequences of $p$-orthogonal polynomials. https://arxiv.org/abs/1910.03039

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