On a Relation Between Classical and Free Infinitely Divisible Transforms

• Autorzy: Jurek Zbigniew J.

Identyfikatory

DOI

10.37190/0208-4147.40.2.9

• Języki publikacji: EN

Abstrakty

EN

We study two ways (two levels) of finding free-probability analogues of classical infinitely divisible measures. More precisely, we identify their Voiculescu transforms on the imaginary axis. For free-selfdecomposable measures we find a formula (a differential equation) for their background driving transforms. It is different from the one known for classical selfdecomposable measures. We illustrate our methods on hyperbolic characteristic functions. Our approach may produce new formulas for definite integrals of some special functions.

Słowa kluczowe

EN

infinite divisibility; free infinite divisibility; convolution semigroups; characteristic function; Voiculescu transform; Lévy-Khinchin formula; Lévy spectral measure; Riemann zeta function; Euler function; digamma function

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2020
• Tom: Vol. 40, Fasc. 2
• Strony: 349--367
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Jurek Zbigniew J.

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

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).