# Product-type non-commutative polynomial states

Banach Center Publications (2010)

- Volume: 89, Issue: 1, page 45-59
- ISSN: 0137-6934

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topMichael 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 -

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