In this paper, we are interested in the following problem. We assume that ${\left\{P_n\right\}}_{n\ge 0}$ is a monic 2-orthogonal polynomial sequence and we analyse the existence of a sequence of 2-orthogonal polynomials ${\left\{Q_n\right\}}_{n\ge 0}$ such that we have a decomposition $P_n(x)=Q_n(x)+a_n{Q}_{n-1}(x),a_n\ne 0,n\ge 1.$ This constitutes the counterpart in the framework of 2-orthogonality of those associated with the Christoffel transformation in the standard case. Some illustrative examples are shown.

中文翻译：

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2正交多项式和Darboux变换。在离散哈恩经典案例中的应用

在本文中，我们对以下问题感兴趣。我们假设${\left\{P_{ñ}\right\}}_{ñ\ge 0}$ 是单数2正交多项式序列，我们分析了2正交多项式序列的存在 ${\left\{{问}_{ñ}\right\}}_{ñ\ge 0}$ 这样我们就分解了 $P_{ñ}（X）={问}_{ñ}（X）+{\mathrm{一种}}_{ñ}{问}_{ñ-\mathrm{1个}}（X），{\mathrm{一种}}_{ñ}\ne 0，ñ\ge \mathrm{1。}$这与标准情况下与Christoffel变换相关联的2正交性构成了对立面。显示了一些说明性的例子。