乘积型非交换多项式态
Product-type non-commutative polynomial states
摘要：
在math/0702157，arXiv：0712.4185中，我们研究了一元多变量非交换正交多项式、它们的递归、正交性状态以及相应的连分数展开式。在本说明中，我们收集了一些例子，展示了这些一般性的结果看起来像非交换多项式的最重要的状态，即各种产品状态。特别地，我们引入了多项式的乘积型状态的概念，它覆盖了所有的非交换泛积，并排除了一些其他熟悉的非交换积，并保证了相应的多项式的一些好的性质。
英文摘要：
In math/0702157, arXiv:0712.4185, we investigated monic multivariate non-commutative orthogonal polynomials, their recursions, states of orthogonality, and corresponding continued fraction expansions. In this note, we collect a number of examples, demonstrating what these general results look like for the most important states on non-commutative polynomials, namely for various product states. In particular, we introduce a notion of a product-type state on polynomials, which covers all the non-commutative universal products and excludes some other familiar non-commutative products, and which guarantees a number of nice properties for the corresponding polynomials.
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