Product-type non-commutative polynomial states

Michael Anshelevich. "Product-type non-commutative polynomial states." Banach Center Publications 89.1 (2010): 45-59. <http://eudml.org/doc/282453>.

@article{MichaelAnshelevich2010,
abstract = {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.},
author = {Michael Anshelevich},
journal = {Banach Center Publications},
keywords = {product states; non-commutative polynomials; continued fractions; orthogonal polynomials; free product; Boolean product; monotone product},
language = {eng},
number = {1},
pages = {45-59},
title = {Product-type non-commutative polynomial states},
url = {http://eudml.org/doc/282453},
volume = {89},
year = {2010},
}

TY - JOUR
AU - Michael Anshelevich
TI - Product-type non-commutative polynomial states
JO - Banach Center Publications
PY - 2010
VL - 89
IS - 1
SP - 45
EP - 59
AB - 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.
LA - eng
KW - product states; non-commutative polynomials; continued fractions; orthogonal polynomials; free product; Boolean product; monotone product
UR - http://eudml.org/doc/282453
ER -