In [AnsMonic, AnsBoolean], 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-2,
author = {Michael Anshelevich},
title = {Product-type non-commutative polynomial states},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {45-59},
zbl = {1215.46040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-2}
}
Michael Anshelevich. Product-type non-commutative polynomial states. Banach Center Publications, Tome 89 (2010) pp. 45-59. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-2/