Title: General Christoffel Perturbations for Mixed Multiple Orthogonal Polynomials Show Chinese title

Title: 混合多重正交多项式的广义克里斯托弗尔摄动

Abstract: Performing both right and left multiplication operations using general regular matrix polynomials, which need not be monic and may possess leading coefficients of arbitrary rank, on a rectangular matrix of measures associated with mixed multiple orthogonal polynomials, reveals corresponding Christoffel formulas. These formulas express the perturbed mixed multiple orthogonal polynomials in relation to the original ones. Utilizing the divisibility theorem for matrix polynomials, we establish a criterion for the existence of perturbed orthogonality, expressed through the non-cancellation of certain $\tau$ determinants. Show Chinese abstract

Abstract: 使用一般常规矩阵多项式进行右乘和左乘运算，这些多项式不需要是首一的，且可能具有任意秩的首项系数，对与混合多重正交多项式相关的矩形测度矩阵进行操作，揭示了相应的Christoffel公式。 这些公式将扰动的混合多重正交多项式与原始的多项式联系起来。 利用矩阵多项式的可除性定理，我们建立了一个扰动正交性的存在性准则，该准则通过某些$\tau$行列式的不抵消来表达。