A note on an article by Artikis (Q1081185)

Let \(p>0\) and \(\phi\) be a characteristic function such that \(\phi (t)=p\int^{1}_{0}\psi (ut)u^{p-1} du\), \(-\infty <t<\infty\), with \(\psi\) as a characteristic function. Further let \(d=\sup \{b>0:\phi\) (t)\(\neq 0\) for all \(t\in (-b,b)\}\). This note identifies the \(\phi\) for which for every \(t\in (-d,d)\), \(\psi\) (t) is a power of \(\phi\) (t), and also discusses some related properties.