# The ${V}_{a}$-deformation of the classical convolution

Banach Center Publications (2007)

- Volume: 78, Issue: 1, page 185-199
- ISSN: 0137-6934

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topAnna 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 -

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