发表机构
Complutense University of Madrid（马德里康普顿斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对单位圆上的$q\times p$矩阵权构造混合型类贝塞尔多重正交多项式，推导其公式、正交性、表示式与递推关系，明确$q=1$时的分解特性。
AI 中文摘要
本文针对单位圆上的$q\times p$矩阵权，构造了一类混合型类贝塞尔多重正交多项式族。与秩一乘积权不同，该矩阵在单位圆的有限子集外具有一般秩$\min\{q,p\}$。当$q=1$时，其倒数伽马矩可恢复多重贝塞尔系统；当$p=1$时，可恢复Wolfs类贝塞尔系统。该矩阵可作为秩一雅可比类系统的缩放马尔可夫-斯蒂尔杰斯极限，尽管区间测度本身无有限极限。针对平衡近对角指标，本文得到了混合$A$和$B$多项式向量的显式公式，证明了它们的正交性和弱正规性，并刻画了分量意义下的强正规性。这些分量具有终止的广义超几何表示；$B$分量还具有有限Kampé de Fériet表示和矩阵罗德里格斯型公式。在单行约化中，二元表示变为由反射型II多重哈恩多项式控制的广义超几何多项式。有限伽马-波赫哈默公式给出了近对角和步长递推系数，对应的带状递推矩阵具有双对角克里斯托费尔分解：下因子由变换后的多项式向量计算，上因子通过有限tau行列式表示。当$q=1$时，所有克里斯托费尔步均保留在多重贝塞尔族内，伽马-范德蒙德行列式给出完整分解。
英文摘要
This article constructs a Bessel family of mixed-type multiple orthogonal polynomials for a $q\times p$ matrix weight on the unit circle. Unlike a rank-one product weight, this matrix has generic rank $\min\{q,p\}$ outside a finite subset of the circle. Its reciprocal-Gamma moments recover the multiple Bessel system when $q=1$ and the Bessel-like system of Wolfs when $p=1$. The same matrix is obtained as a scaled Markov-Stieltjes limit of a rank-one Jacobi system, although the interval measures themselves have no finite limit. For balanced near-diagonal indices, explicit formulas are obtained for the mixed $A$ and $B$ polynomial vectors. Their orthogonality and weak normality are proved, and componentwise strong normality is characterized. The components have terminating generalized hypergeometric representations; the $B$ components also admit finite Kampé de Fériet representations and a matrix Rodrigues-type formula. In the one-row reduction, the bivariate representation becomes a generalized hypergeometric polynomial governed by a reflected type-II multiple Hahn polynomial. Finite Gamma-Pochhammer formulas give the near-diagonal and step-line recurrence coefficients. The corresponding banded recurrence matrix has a bidiagonal Christoffel factorization: the lower factors are evaluated from transformed polynomial vectors, while the upper factors are expressed through finite tau determinants. When $q=1$, every Christoffel step remains within the multiple Bessel family, and Gamma-Vandermonde determinants yield the complete factorization.
