We study deformations of the classical convolution. For every invertible transformation T:μ ↦ Tμ, we are able to define a new associative convolution of measures by . We deal with the -deformation of the classical convolution. We prove the analogue of the classical Lévy-Khintchine formula. We also show the central limit measure, which turns out to be the standard Gaussian measure. Moreover, we calculate the Poisson measure in the -deformed classical convolution and give the orthogonal polynomials associated to the limiting measure.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-14,
author = {Anna Dorota Krystek},
title = {The $V\_a$-deformation of the classical convolution},
journal = {Banach Center Publications},
volume = {75},
year = {2007},
pages = {185-199},
zbl = {1140.46326},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-14}
}
Anna Dorota Krystek. The $V_a$-deformation of the classical convolution. Banach Center Publications, Tome 75 (2007) pp. 185-199. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-14/