The $V_a$-deformation of the classical convolution

• Autorzy: Anna Dorota Krystek
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L53: Noncommutative probability and statistics
• 46L54: Free probability and free operator algebras
• 60E10: Characteristic functions; other transforms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 78
• Numer: 1
• Strony: 185-199

Daty

wydano

2007

Twórcy

autor

Anna Dorota Krystek

• Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/bc78-0-14