Convolutions related to q-deformed commutativity

Anna Kula. "Convolutions related to q-deformed commutativity." Banach Center Publications 89.1 (2010): 189-200. <http://eudml.org/doc/282440>.

@article{AnnaKula2010,
abstract = {Two important examples of q-deformed commutativity relations are: aa* - qa*a = 1, studied in particular by M. Bożejko and R. Speicher, and ab = qba, studied by T. H. Koornwinder and S. Majid. The second case includes the q-normality of operators, defined by S. Ôta (aa* = qa*a). These two frameworks give rise to different convolutions. In particular, in the second scheme, G. Carnovale and T. H. Koornwinder studied their q-convolution. In the present paper we consider another convolution of measures based on the so-called (p,q)-commutativity, a generalization of ab = qba. We investigate and compare properties of both convolutions (associativity, commutativity and positivity) and corresponding Fourier transforms.},
author = {Anna Kula},
journal = {Banach Center Publications},
keywords = {convolution; positive definiteness; -normal elements; non-commutative probability; deformations},
language = {eng},
number = {1},
pages = {189-200},
title = {Convolutions related to q-deformed commutativity},
url = {http://eudml.org/doc/282440},
volume = {89},
year = {2010},
}

TY - JOUR
AU - Anna Kula
TI - Convolutions related to q-deformed commutativity
JO - Banach Center Publications
PY - 2010
VL - 89
IS - 1
SP - 189
EP - 200
AB - Two important examples of q-deformed commutativity relations are: aa* - qa*a = 1, studied in particular by M. Bożejko and R. Speicher, and ab = qba, studied by T. H. Koornwinder and S. Majid. The second case includes the q-normality of operators, defined by S. Ôta (aa* = qa*a). These two frameworks give rise to different convolutions. In particular, in the second scheme, G. Carnovale and T. H. Koornwinder studied their q-convolution. In the present paper we consider another convolution of measures based on the so-called (p,q)-commutativity, a generalization of ab = qba. We investigate and compare properties of both convolutions (associativity, commutativity and positivity) and corresponding Fourier transforms.
LA - eng
KW - convolution; positive definiteness; -normal elements; non-commutative probability; deformations
UR - http://eudml.org/doc/282440
ER -