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Dur\\'an, Manuel D. de la Iglesia","submitted_at":"2013-07-04T13:41:15Z","abstract_excerpt":"Given a sequence of polynomials $(p_n)_n$, an algebra of operators $\\mathcal{A}$ acting in the linear space of polynomials and an operator $D_p\\in \\mathcal{A}$ with $D_p(p_n)=np_n$, we form a new sequence of polynomials $(q_n)_n$ by considering a linear combination of $m$ consecutive $p_n$: $q_n=p_n+\\sum_{j=1}^m\\beta_{n,j}p_{n-j}$. Using the concept of $\\mathcal{D}$-operator, we determine the structure of the sequences $\\beta_{n,j}, j=1,\\ldots,m,$ in order that the polynomials $(q_n)_n$ are common eigenfunctions of an operator in the algebra $\\mathcal{A}$. 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