IPM - Institute for Research in Fundamental Sciences

“School of Mathematics”

Paper IPM / M / 7311

School of Mathematics

Title:

Solution to a functional equation and its application to stable and stable-type distributions

Author(s):

Status:

Published

Journal:

Statist. Probab. Lett.

Vol.:

Year:

2004

Pages:

1-9

Supported by:

IPM

Abstract:

The main result of the paper completely characterizes all continuous complex-valued functions φ(t) with domain \mathbbR⁺ or \mathbbR satisfying

φ(t)=(φ(a₁t))^γ₁=(φ(a₂t))^γ₂

where a₁ ≠ 1, a₂ ≠ 1,γ₁, γ₂ are positive numbers with irrational [(loga₁)/(loga₂)].

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