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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-11,
author = {Anna Kula},
title = {Convolutions related to q-deformed commutativity},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {189-200},
zbl = {1210.28018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-11}
}
Anna Kula. Convolutions related to q-deformed commutativity. Banach Center Publications, Tome 89 (2010) pp. 189-200. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-11/