Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Product-type non-commutative polynomial states   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.

23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph