The $V_a$-deformation of the classical convolution

Anna Dorota Krystek. "The $V_a$-deformation of the classical convolution." Banach Center Publications 78.1 (2007): 185-199. <http://eudml.org/doc/281697>.

@article{AnnaDorotaKrystek2007,
abstract = {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 $μ\{*_T\}ν = T^\{-1\}(Tμ*Tν)$. We deal with the $V_a$-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 $V_a$-deformed classical convolution and give the orthogonal polynomials associated to the limiting measure.},
author = {Anna Dorota Krystek},
journal = {Banach Center Publications},
keywords = {convolution; deformations; moment-cumulant formulae; limit theorems; Lévy-Khintchine formula},
language = {eng},
number = {1},
pages = {185-199},
title = {The $V_a$-deformation of the classical convolution},
url = {http://eudml.org/doc/281697},
volume = {78},
year = {2007},
}

TY - JOUR
AU - Anna Dorota Krystek
TI - The $V_a$-deformation of the classical convolution
JO - Banach Center Publications
PY - 2007
VL - 78
IS - 1
SP - 185
EP - 199
AB - 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 $μ{*_T}ν = T^{-1}(Tμ*Tν)$. We deal with the $V_a$-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 $V_a$-deformed classical convolution and give the orthogonal polynomials associated to the limiting measure.
LA - eng
KW - convolution; deformations; moment-cumulant formulae; limit theorems; Lévy-Khintchine formula
UR - http://eudml.org/doc/281697
ER -